Are 15 year old NiMH rechargeables still worth using?

A 1.1 to 1.2 volt reading on those old cells is actually quite typical for NiMH types that have been sitting in storage for that long. It definitely doesn't tell you much about their remaining capacity, though; it just means they have drained significantly and have entered a storage state. The reason they aren't dead is likely because they were kept in a relatively cool, stable environment, which slows down the chemical self-discharge process. Most rechargeable cells lose a lot of their charge over time, even if they don't fail entirely.

Regarding the two that read zero, you should definitely give them a try before tossing them. Sometimes a battery that reads totally dead will show a trickle of life after it's been subjected to a full charge cycle. Charging them, even if they are old, is the only way to see if there is any hidden capacity left. If they refuse to hold a charge, though, just toss them. For those two, the risk of them simply failing during the charging process is low, but it's better to start with the 1.1V units you already have.

Using these in solar path lights is a good low-risk idea. Those types of devices pull very little current, which means you won't be stressing the cells as hard as they woud be in a high-draw device like a flash or a professional-grade camera. Because they are only handling short, intermittent bursts of power, it gives them a much better chance of lasting through a few more light cycles. If you just cycle them a few times, you'll quickly learn if the current they provide is stable and consistent.

In general, if you are going to use these for something low power like those lights, giving them a proper, full charge first and then running a discharge cycle is a simple way to see if they are worth keeping. If they hold a decent percentage of their capacity after a few cycles, they are fine. If they just drop off a cliff in voltage after a few minutes, they are definitely at the end of their life.

I've had a similar thing happen, but mine were just sitting in a box in the shed instead of a garage. I was worried that the temprature swings in the shed might have damaged the chemistries more than a garage. Since the cells were probably storing in varied conditions, I wonder if there's any way to check if they handled different temperatures well over the years, or if that just doesn't matter for NiMH. My main concern is whether the inconsistent storage enviornment could have caused internal corrosion or something similar that wouldn't show up in a simple voltage test. I'm just trying to avoid putting anything that might fail right under the solar panels and ruining the setup.

I think you should check the physical condition of the contacts for any white powdery substance, which would suggest environmental exposure to moisture or significant heat cycling, as that specific chemical stress can accelerate cathode degradation independently of simple shelf life. Furthermore, since you are considering these for low-power lights, you should observe if they maintain a steady voltage curve during a full discharge test, rather than just focusing on the initial capacity percentage. A battery with high internal resistance will often fail much sooner even if it technically holds a charge.

Update: cycled the four that read 1.1 or better and they're holding a charge decently, so the voltage really was just a storage thing like you said. Two of the no-name cells had that white crusty stuff around the positive end though. Is that corrosion a sign the whole batch from that box might leak eventually, or just those two?