I believe the answers to these questions are all positive. This kind of problem was discussed by Groszek and Laver in *Finite groups of OD-conjugates* [Period. Math. Hungar. 18 (1987), 87-97, [MR0895774](http://www.ams.org/mathscinet-getitem?mr=895774)]. Answering a question of Mycielski, they show that there can be two sets of reals $x,y$ such that $\lbrace x,y\rbrace$ is ordinal definable but neither $x$ nor $y$ is ordinal definable. They also prove a lot of other things about OD conjugates.