Very little information is given about this side of the family. Harry saw a grandfather among the various relations in the Mirror of Erised, but we haven't been given any more than that. It would seem that all the Potter family were wizards, and that they're all dead (PS12). JKR has told us that there was nothing sinister about the deaths of Harry's Potter grandparents (TLC). Harry's grandfather was in Gryffindor, like his son and grandson (DH34).
Sirius Black ran away from home at the age of 16 and moved in with James' family. He said that James' parents took him in as "a second son" (OP6), which strongly suggests that James was their only son.
Lily Evans had a sister named Petunia Evans. Lily was a Muggle-born witch. After Lily was invited to join the magical world at Hogwarts, Petunia corresponded with Albus Dumbledore about being admitted at Hogwarts. After being politely denied Petunia resented her sister and the way their parents seemed to approve of Lily's magical ability calling her a freak (DH33). Petunia is married to Vernon Dursley and has one son named Dudley.