I was told I have a tilted uterus too. I'm 28 weeks, and with all the aches and pains that go along with pregnancy, I can't say I've felt anything that would be correlated to a uterus "straightening out". My doctor tolde me some women just have this, and really doesn't affect anything. I'm pretty sure I've felt my uterus stretching...not straightening. I wouldn't worry about it.
I have a tilted uterus...and have also heard that it straightens out by the end of hte first trimester. It didn't happen my first pg, but I was VERY surprised and upset when they had to feel the size of my uterus at my first OB checked by doing a rectal exam.
Also, I'm not sure if it's related at all, but I had pretty bad back labor my first pg...kneeling on all 4's seemed to take alot of pressure of my back.
I don't think you have anything to worry about. I've had a tilted uterus since after the birth of my first child and have had 2 since and like they say, it straightens itself out during pregnancy. I never noticed any change and after I gave birth my uterus would be tilted again. Never had any pain from it though. Good Luck!