You have good responses from others trying to use your original words, so I'll approach from a different 'angle'. These sentences are ambiguous because there are different usages for
ever, since, and
ever since.
ever =
at any time
since =
after the time that... OR because
ever since =
at any time after
As a result, your example sentences can mean different things.
1.
I haven't done it ever since I was asked not to.1a. I haven't done it ever, since I was asked not to. I was asked to not do it before I would/could have done it. For that reason I have never done it. Better as: I've never done it, because I was asked not to.
1b.
I haven't done it ever since I was asked not to. I used to do it. I stopped doing it after I was asked to not do it. Better as: I stopped doing it when I was asked not to. Or: I stopped doing it when asked. Or even, with context: I stopped when asked.
2. I hadn't done it ever since I was asked not to do it. Response(s) the same as #1. The "do it" is understood in #1. The timeline of events merely shifts a step back in time.
3. They shouldn't have done it ever since they were asked not to do so.
3a. They shouldn't have done it ever, since they were asked not to do so. Pretty much the same as 1a above. They were asked to not do it before they had a chance to do it. For that reason, they should never have done it, but they did. This could be clarified by re-ordering the sentence: They were asked not to do it, so they should never have done it.
3b. They shouldn't have done it ever since they were asked not to do so. They were doing it. They were asked to not do it. They kept doing it, but they shouldn't have. Better as: They should have stopped doing it after they were asked to stop.
