22 is a microscopic 50.3%-49.7% favorite against one random hand. 22 is an underdog against 85s. 22 is an underdog against 2+ random hands. 22 often has an information disadvantage in a normal pot so it is hard to bet for value.
AK is a significant favorite over 1 or more random hands. AK is a big favorite over many good hands your opponents will play for a raise. AK can often semibluff cheaply or bet for value after the flop.
22 does slightly better than AK when your opponent has Q2-32, 22, or AA, and the AA shouldn't count because AK blocks half of the AA combinations. AK does better against the other hands your opponent can hold, often by a huge amount.
If you were playing 2 card stud, 22 would be the 13th best hand. Since you are playing a 7 card stud variant, 22 is at best a mediocre hand which is often overvalued, while AK is a very good hand. According to some of the PokerRoom stats, on average,
22 loses money in every position (although at some stakes and some positions, it comes out slightly ahead, which may be noise).
AKo wins money in every position.