I would've thought the quickest way to do it is to drop the files onto a USB stick. If it's a Divx or Xvid file then it should be playable on either the 360 or PS3. If it's a high-definition MKV file then
mkv2vob will convert it into a format suitable for playing on the PS3. You
can use mkv2vob to convert it into a file that the 360 can play but it'll take longer (as it has to re-encode the video, which it doesn't have to do for the PS3).
Personally I'm more than happy using an old Xbox and XBMC for most of my media playing (due to its ability to play DVD images off network drives, subtitle support, etc.) although it helps that I don't have an HDTV so don't have any high-def files to watch -- if I did then I'd be looking at getting one of those WD high-def boxes, a Popcorn Hour, an AppleTV (to hack with XBMC) or something like that.
As for finding things, as Trousers says newsgroups are awesome although depending on your news server's retention (ie. how long things hang around for) you may struggle to get anything older than 3-6 months. If you happen to have Virgin cable then their newsgroups are operated by a third party (Highwinds) and you get 7-day retention with unlimited downloads (they don't monitor what you download either
) -- the retention is a bit rubbish but if you keep on top of things then you'll be alright (it would more than suffice for keeping up with TV programmes, for example), and unlimited download capacity is very good (many providers do limit how much you can get per month). If you go the newsgroup route then I use
newzleech.com to search for NZB files (which tell your newsgroup program the files to download) and
alt.binz to download the files. I also use sites like zerosec.ws, scnsrc.net and rlslog.net to keep an eye on what's out there.