As long as all the games are still inside the Steam install folder, then all you need to do on your new computer is open Steam and install all the games that you have in your Steam install folder as if you were installing them from scratch. The installer will then detect and local game content and then download any files that it doesn't find - 90% of the time though, it will find all the files fine.
Origin I think already detects your games as installed, but i'm not sure since i've never had to do this with Origin games. It might also work the same way as Steam. Uplay I have no idea unfortunately because I think it's a shit piece of software, but if Straw hasn't had any problems then i'm sure you won't either.