My mother gave me a bottle of menora oil that was in the house. I know that my father is not makpid, and gezeila is certainly not a concern. The question is whether I was koneh the oil, or is there a problematic lack of daas makneh?
There is no problem. Since this is a small gift, your mother has the right to give it away, and you are koneh based on her daas and the implied consent of your father.
Beyond this, according to many authorities, including the Mishnah Berurah (67:2 – the problem of stolen oil is the aveirah involved, and not the question of ownership) and the Beis Yitzchak (Yoreh De’ah 145) there is no need to actually own the oil – though this is not agreed on by all authorities (for instance, see Ran, Pesachim 7a).
Best wishes, and apologies for late reply (due to a technical hitch the reply to a number of questions was delayed).