As to SoundCloud, I don't know, I'm afraid.
However, as to YouTube, I believe that you just paste the URL of the video--the full URL, not a shortened version--into a post, and the forum software should embed it for you. Like this:
http://www.youtube.com/watch?v=<SOME VIDEO ID HERE>
In Firefox (I don't know about other browsers; try it!) you should be able to get this URL by going to your channel, finding the relevant video, right-clicking on it, and selecting "Copy Link Location".
If you're watching the video, simply copy the URL in the address bar (removing any additional commands, like a time-offset). Note that, while you can get a video URL from a video that is playing by right clicking in the viewing area and selecting "Copy video URL", this seems to give a shortened URL, which may or may not work (I don't know, myself).