How does the Commander interact with Banishing Light or Oblivion Ring?
Yes, you are correct that in the situation you describe, Banishing Light will return the commander from the command zone to the battlefield, but Oblivion Ring will not do that.

The main reason that it works this way is rule 610.3:


  Some one-shot effects cause an object to change zones “until” a specified event occurs. A second one-shot effect is created immediately after the specified event. This second one-shot effect returns the object to its previous zone.


Banishing Light's effect is one of these. The important thing to note is that returning the object to its previous zone does not depend on which zone it originally moved to.

Oblivion Ring, on the other hand, has two separate abilities, which are called linked abilities. Rule 607.2a describes how this kind of linked ability works:


  If an object has an activated or triggered ability printed on it that instructs a player to exile one or more cards and an ability printed on it that refers either to “the exiled cards” or to cards “exiled with [this object],” these abilities are linked. The second ability refers only to cards in the exile zone that were put there as a result of an instruction to exile them in the first ability.


Because Oblivion Ring's second ability refers to "the exiled card", it can only find cards that are actually in the exile zone when it resolves.