You should not have a 20A receptacle on a 15A line to start with.
Also, could be a really funky installation. I had a receptacle that fed the lead to a second one. The second one didn't work at all, but the first one showed 110V hot to ground. However, nothing would turn on that i plugged in. I pulled it out, and here's what they had done. The hot went to switch one as did ground. The neutral went straight to switch two but wired at the hot terminal and a neutral wire was jumpered from switch one to switch two. I think the one who did that was on crack that day. So like jmans said, if you put a tester in the hot terminal and it lights up or you measure hot to ground and get voltage, but nothing turns on, sounds like you're missing a neutral connection in there.