Hmm, during 5 weeks between D&C and AF I had 3 positive OPKs. I used clearblue digitals and checked the lines manually as well. They were definitely all positive. Personally, I don't think I ovulated at all that cycle. I think my body tried, came close, but failed every time. The test picks up on the surge of LH, which I assume happened for me, but it can't tell you if you actually ovulated. That is why I tracked my temperature the next cycle so that I would actually know.
So I'm not sure if those were false positives from the HCG in my system, if I was very close to ovulating several times and it just didn't happen, or if one of them was a real ovulation. I was still getting positive HPTs until 4 weeks post-D&C so those hormones were definitely lingering in my body for a while.
Oh and as for what a positive looks like. On OPKs you will always get two lines, but you'll know it is a positive when the test line is as dark as or darker than the control line. That said, some women never get a dark line so they consider it positive when it is almost as dark as the control. You would need to track for a few cycles to find out if you fall in this category though.
ETA I'm really not an expert so if I got anything wrong, someone please correct me!