See Autodraft Cards

Is there a way I can see who was on someone else's Autodraft card after the draft has run?

Not a legal way. There have at various times been reported URLs that would accomplish it that were in theory only for use by beta testers. But it is my understanding all those have now been blocked.

I doubt any manager here would want you to see their actual autodraft card.

You could always ask though. If they do not object I assume they will tell you. If they do object then well that is information you should not have.

In one of my Franchise Leagues I had a manager Autodraft the wrong team, so we needed up with TWO Pittsbugh Pirates teams. I was trying to see who the correct Pirates had auto drafted so the correct Pirates manager could get their rightful players.
SOM worked it out instead.

I want to see the other draft cards prior to the draft

Yep, there is a way to see your draft card post draft.

1) Navigate to your team page
2) paste the draft rank your team url into the browser - http://365.strat-o-matic.com/team/draft/rank

The browser remembers your team ID in the cache and then accesses the draft card even though the link isn't accessible anymore from the team pages.

It only works for your team.