Any oils that have no smell at all you wouldn't want to use as they'd be the wrong type of oil to use in finishing.
Oils of the right type, all of them AFAIK, have some odour as BB says above. It's not particularly strong and it does go away in time, and I don't think it's objectionable but some people are very particular about this sort of thing. Take the classic scent of linseed oil which many remember from their youth (maybe from cricket bats or window putty), lots of people love it and sort of can't understand how anyone wouldn't love it too, but it makes some people gag so there you go!