Rules as written, anyone can spend an Omen at any time to influence the dice. So you can spend multiple Omens back to back to try to pass an essential roll, and you can use an Omen to reroll a friend's failure.
You can also theoretically use Omens to influence the results of roll tables and stuff like that.
Of course, groups can absolutely change this. And individual modules can specify stuff like "you can only use one Omen per test."