Previously, the only way to do strikethrough or tables on Tildes was by using HTML. I've updated the markdown parser now so that it supports the methods of doing them through markdown. The Formatting help page on the docs has been updated as well with info about how they work.
I don't think there should be any conflicts between strikethrough and linking to groups, but it's possible that there are some weird edge cases, so please let me know if you notice anything. Generally, strikethrough requires you to have two tildes both before and after the text you want to strike out, whereas group links will only have one before. So something like
This ~~should work~~ doesn't work will result in
should work instead of a link to a group named ~should.