Thought it was likely a bug that it didn't create when there was this massive cave there. After putting down close to 1000 torches, and finding 50 something diamonds on accident I have still not searched through it all, but had seen no sign of a stronghold. The cave went back and forth and down to bedrock many places, and at points I could view blue sky. After digging sideways for quite a while I managed to dig myself a stair down to the side of the cave, and started exploring it. I figured it should be easy to spot the stronghold down there, assuming it generated like nether fortresses and would stick out of the cave somewhere. Dug down ~10 blocks and suddenly I was looking down from the roof of the most massive cave I've encountered up until now. Traveled over to the intersection point, that was pretty close to the top of a decently sized hill. Then wrote down the formulas for the two lines and calculated the intersection point. Then I moved 45 degrees on that line for a while, and threw from a position useful to triangulate and did another throw. Recorded how many blocks away it was in X and Z coordinates. Threw one and tried to spot a block the eye traveled right over. In my current game, I decided to triangulate the position from Ender eye throws. Those strongholds can be a bit pesky to find if you're out of luck. Maps can also help strongholds are generally fairly large so you can travel to the edge of the mapped area and look around, then repeat from the edge of the newly mapped area (I carry a map with me while caving so I can see where I've been in general everything within the mapped area has been explored, except for a 128 block boundary around the edges). Mineshafts (also assuming they generated like they did until release 1.6.4 I know that caves were unchanged) become more common as you go further from 0,0 and at some point the underground becomes virtually infinite, if not so interconnected that you can easily travel in a particular direction.

Otherwise, I've found at least a dozen strongholds by caving, although each one takes weeks of playtime (fully exploring the entire area outwards from spawn/0,0, and not specifically searching for them), which could be significantly reduced by exploring caves as sparsely as possible to get through the area (don't go through every cave/mineshaft, just what you need to go in a particular direction. Assuming they generate like they did until release 1.9 they will be 640-1152 blocks away from 0,0, so you know you won't find anything outside of that area, and they are in a triangular formation so once one is found the others will be about 120 degrees apart.

Stronghold minecraft