Loose headset?
I'd also check the frame/fork for cracks. Possibly a cracked steerer tube.
That's my guess. Pull the fork and check the bearings in the head tube real good. Could be a single bearing that chipped or broke and is working it's way around the race causing problems when everything lines up with the missing chunk in the bearing. One of the bikes I scavanged for parts this summer had a bad single ball bearing in the bottom bracket.
Sounds like something is getting to a loose point, causing havoc, then setting itself tight again before you can track it down.