With the understanding that I'm pretty good at this sort of thing, but far from all-knowing...
1) I was a partner in the law firm, after all.
Correct as it is. The words after all make up a parenthetical, an additional few words not necessary for the reader's comprehension of the sentence.
2) I was a partner in the law firm after all.
Incorrect. When the parenthetical is not separated by a comma (or a pair of commas if it comes mid-sentence), it lets the reader misinterpret and invites a sort of mental stumble. I was a partner in the law firm after... leads the reader to expect an event, perhaps someone else making partner, or something notable about the law firm, after which the speaker was made partner. This is the mental stumble you want to avoid. I was a partner in the law firm after all can me misinterpreted as the speaker being the very last person to become partner.
3) Soccer could be a tiring sport, as well.
Incorrect. As well is not a parenthetical but necessary for the sentence's point, that in addition to whatever sport was previously mentioned, soccer is also tiring.
4) Soccer could be a tiring sport as well.
Correctomundo. (How do they run constantly for so long?)
5) Timmy wanted to go fishing, too.
Correct but rapidly going out of style, never mind what I was taught as a child. Many publishers' house styles now eliminate the comma before a final too. You won't be considered wrong if you include it, but if that's what you choose, make sure you're consistent.
6) Timmy wanted to go fishing too.
Correct in terms of house style at most publishers.
7) Marcy didn't know which shirt to choose, either.
Correct, although like too, the comma before either is losing ground. The forward-thinking concept is that without the comma, the added word becomes a more integral part of the total concept.
8) Marcy didn't know which shirt to choose either.
Correct in terms of most house styles. As with too, pick which way you like it and be consistent.
Maryn, expecting Chase to mosey in here soon enough