If I post a backlink on a website that isn't in my niche but it isn't nofollow, will it still help my website? I know posting backlinks on websites in the same niche is very good.
Certainly, relevant backlinks are more beneficial but even not so relevant backlinks are beneficial. I have practically verified this by visiting the websites of many webmasters who leave comments on my blog and discover that some of them are high PR sites even from irrelevant niches to mine. Apparently, they must have acquired their high PR in this way amongst others, otherwise they will not continue posting to irrelevant sites.
If you can get your hands on a link then do it. But if you find one that has relevancy then it will be even better.
If all your links come from non-related areas and you have a whole bunch of them, that could possibly be a negative in the long run.