Draupadi had one son from each Pandava brothers. Their names are Prativindhya, Sutasoma, Shrutakarma, Satanika and Shrutasena. They are known as Upapandavas. They are described as formidable warriors. After the death of Duryodhana, Ashwattama, Drona’s son, and two remaining Kaurava warriors, decided to avenge their defeat by destroying the Pandava camp. They attacked the Pandava camp in the night while they were asleep. All the Upapandavas were killed. The Pandavas, Draupadi and Krishna were not in the camp. It was the most heartbreaking event for Draupadi. As per folktales, Draupadi had a daughter called Suthanu as well, from Yudhishthira. She married Swarabhanu, Krishna-Satyabhama's son. The Wikimedia image is of Raja Ravi Varma’s painting of Draupadi and the five Pandavas.

Krishna & the Pandavas chased Ashwatthama after he slaughtered Upapandavas in their sleep. Ashwatthama & Arjuna used the divine weapon ‘Brahmasiras’ on each other. Fearing destruction, Vyasa & Narada intervened and asked them to retract their weapons. Arjuna did. However Ashwatthama maliciously redirected the weapon on the womb of Abhimanyu’s widow Uttara who was pregnant. Krishna intervened and revived the dead child (who was also his grandson).
The revived child grew up to be Parikshit. He succeeded Yudhistira and ruled magnificently for sixty years. Atharvaveda celebrates a king named Parikshit who brought prosperity to the land and systematized Vedic culture.
Ashwatthama was stripped off the magnificent gem that adorned his head and cursed to live a miserable and lonely life without death.
The Wikimedia image is of an unknown 19th cent CE painting from the Kashmir school showing Parikshit before Sri Vishnu.

Janmajeya was the son & successor of Parikshit and thus the great grandson of Arjuna. The Anukramanika (1st chapter) of Mahabharata says that Janmajeya held a sarpa satra (serpent sacrifice). Janmajeya held the satra to avenge his father’s death by snake-bite due to a curse. In the Satra, Vaisampayana, Vyasa’s disciple narrated the epic that he had learnt from his guru. It was heard by Ugrasravas who later recited the epic at Rishi Saunaka’s 12-year yajna at Naimisaranya forest, near modern Lucknow.
Ugrasravas’ version of Mahabharata is what we read and hear now. The critical edition omits this chapter but the transmission chain is accepted.
The Wikimedia image is of the sarpa satra, by an unknown artist circa 1920s.

Ekalavya was killed by Krishna. Ekalavya was an ally of Jarasandha. He attacked Dwarka after Krishna had assisted in Jarasandha’s slaying. Ekalavya was killed in this battle. Following Jarasandha’s death, Yudhistira did the Rajasuya yajna in which Eklavya’s son Ketuman was invited. Ketuman fought on the side of the Kauravas in the great war and was slain by Bheema.
Mahabharata refers to Eklavya’s death in two places, Udyog Parva and Drona Parva. Krishna himself tells Arjuna in Drona Parva that he had killed Ekalavya for the benefit of Pandavas.
Source: KM Ganguly’s English translation of Mahabharata

Abhimanyu was the son of Subhadra & Arjun. On the 13th day of the war, he broke the famous Chakravyuha and continued to fight. He died only when seven senior Kauravas together struck at him. Dushashana’s son dealt the final blow. He in turn died at the hands of Draupadi’s eldest son, days after.
Mahabharata also mentions that Brihadbala, the king of Kosala was killed by Abhimanyu on that day. Later Puranic texts suggest that he was the last descendant of Sri Rama’s Ikshvaku dynasty. We know from Kalidasa’s immortal ‘Raghuvansham’ that like many other great families, Rama’s dynasty had degenerated towards the end.
The Wikimedia image of a painting by Pratap Mullick is the most famous representation of Abhimanyu.

Duryodhana’s son, Lakshmana was a prince and was unlike his father. He met a brave end at the hands of Abhimanyu. Puranic texts say that he also had a twin sister Lakshmanaa. Duryodhana’s wife is also not named in the Mahabharata, though it says that she was kidnapped and married to her husband. Later texts name her Bhanumati. In some folk stories, she marries Arjuna after the war to end the hostility in the Kuru family. Popular lore laments the bad luck of Bhanumati – forcibly married, lost her husband & son to war and made to marry the enemy who widowed her. She is the symbol of how a woman keeps a family together in the face of setbacks. A popular Hindi saying is,
“कहीं की ईंट, कहीं का रोड़ा, भानुमति ने कुनबा जोड़ा”
“Kahin ke eent, Kahin ka rorda, Bhanumati ne kunba joda”
From disparate elements, Bhanumati created a family.
The Wikimedia image is of Raja Ravi Varma depicting Abhimanyu killing Lakhsmana.

Duryodhana’s daughter Lakshmanaa (or Laksana) is not mentioned in the Mahabharata. But the Harivamsam (annexure to the epic) and the Bhagvatam have her story. Samba was the son of Krishna & Jambavati. Hearing about the Svayaṃvara of Lakṣhmaṇaa, Samba went to Hastinapura and took her by force. Duryodhana captured him but he was rescued by Krishna who took the bride and the bridegroom to Dvaraka. They had ten sons.
Samba was handsome, wicked & a womanizer. He was cursed by Krishna to have leprosy. To cure himself, Samba is said to have established the practice of sun worship at Sambapura on river Chandrabhaga (Chenab). The establishment of the famous medieval sun-temple at Multan (destroyed in the Middle Ages) is sometimes attributed to him. The image is of the 4th cent CE panel at Hyderabad Museum depicting Samba (2nd from right) and other Vrishni (Yadava) heroes.
Source:https://www.wisdomlib.org/hinduism/compilation/puranic-encyclopaedia/d/doc241914.html

Ghatotkacha was the son of Bheema & Hidimba. Bheema killed the rakshasa Hidimb during their exile after the burning of the wax palace. Hidimba is the sister of Hidimb. Ghatotkacha was the eldest of the Pandava children. He was a great warrior with magical powers. On the 14th day, the battle continued after sunset. That is when Ghatotkacha wreaked havoc on the Kauravas. As a rakshasa, he was almost invincible at night. Finally, Karna had to use his magic weapon ‘saktayudha’ to fell him. Karna had got this unerring single use weapon from Indra. Karna intended to use it on Arjuna, but was forced to stop Ghatotkacha with this weapon. Krishna celebrated Ghatotkacha’s sacrifice by saying that the loss of ‘saktayudha’ had probably saved Arjuna from death. Ghatotkacha is the subject of many popular folk tales, one of which was turned into the super hit Telugu/Tamil film ‘Maya Bazaar’ (1957), starring superstar NT Rama Rao. The image is of a poster of this film.

Arjuna was exiled for a while as he broke the rule of not invading the privacy of any of the Pandava brothers when they were with Draupadi. During the exile he married a Naga princess Ulupi and a Manipuri (Manalurapura) princess Chitrangada. Chitrangada’s son Babhruvahana went on to become king.
After winning the war, Arjuna accompanied the horse of the ashwamedha yajna which wandered to Manalurapura. Ulupi encouraged Babhruvahana to fight though he was unwilling to fight his father. Arjuna fought mildly but an excited Babhruvahana tried to impress his father and felled him. Chitrangada blamed Ulupi for the fight. Ulupi then got the gem that revived Arjuna. She told Arjuna that this episode is an atonement for killing Bhishma.
The Wikimedia image shows Babhruvahana approaching Arjuna, from a Persian translation.

Vyasa’s Mahabharata mentions Karna’s family life in passing. He married a woman chosen by his adoptive father, Adhiratha and had two sons Vrsasena & Susena.
Vrsasena was a brave man who faced Arjuna on the 17th day just before the final battle between Arjuna & Karna. Arjuna shot ten arrows that tore apart Vrsasena’s bow, arms & head. Arjuna taunted Karna that he killed his son in front of him while Karna had killed Abhimanyu in his absence.
The Wikimedia image is of a 18th cent CE miniature of the Basholi school depicting the disrobing of Draupadi. Vrsasena is shown sitting 2nd from right.

36 years after the Mahabharata war, Dwarka witnessed a civil war among the Yadavas. A great flooding by the sea destroyed the city. Most of the Yadavas including Krishna & Balarama perish. Arjuna arrived to rescue the remnants. On his way back, he was unable to protect the Yadava survivors from roving dacoits in the Panchnada (Punjab) region.
Arjuna is able to save only some Yadavas and he rehabilitates them. Krtvarma’s son is established at Mrttikavata, Satyaki’s son on the banks of Sarasvati and some more. Vajra, son of Aniruddh & Usha, is made the king of Indraprastha. Aniruddha was the son of Pradyumna, Krishna’s eldest son. Thus, Arjuna manages to save Krishna’s lineage from extinction.
The Wikimedia image by kunalmehra7 is of the Dwarkadhish temple which as per legends was established by Vajra.

Barbarik’s story has no mention in Vyasa’s work. It is a legend which is now very popular in Rajasthan. Barbarik was the son of Ghatotkacha & Princess Maurvi. Barbarik was said to be invincible and he could tilt the balance of any side that was temporarily weaker. Logically, if he had participated in the war, only he would have survived. To avoid this, Krishna is supposed to have asked Barbarik to severe his head. He granted him a boon that he would be able to watch the war through his severed head. He would also be known by Krishna’s own name, Shyam Ji in the kaliyug and would be worshipped in his own form.
The Khatu Shyam Mandir stands where Krishna is supposed to have drowned his head. Historically, the local king first built this temple in the early 11th cent CE.
Source: https://www.tourism.rajasthan.gov.in/khatu-shyam-temple.html