The thing about oil leaks is that many times, the oil only leaks while under pressure or circulating, not while sitting in the driveway.
I was "burning" 1 qt every 1000 miles. I just assumed it was burning, b/c I had the same symptoms as you - oil loss, no drips, seemed to use it faster if I dogged it.
Then I did my rod bearings. In replacing the rod bearings, it got new pan gaskets, oil level sender, and much TLC upon reassembly - cleaning, proper torque, etc. I found, too, that the oil level sender had come somewhat loose - it wasn't backing out, but I could've unscrewed it by hand.
My oil consumption is now negligible - I did a 1200 mile road trip and didn't burn a drop! At 125k, you might as well do the rod bearings anyway, and **** all those birds...