Why are all the toilets in my house running intermittently?
You have to diagnose why the toilets are running, but given that multiple toilets have started running simultaneously, I'm guessing your water pressure is too high. This can be due to a falling PRV or a missing or failing expansion tank. See this answer for the steps to check an expansion tank. This answer may also be helpful. If you find your water pressure is well over 60psi (I believe) all the time, then you need a PRV (or to replace your existing one).

If checking your water pressure shows that it's never high, then it's time to diagnose the toilets. If the float valve is adjusted too high and allows the water to reach the overflow, then you may be losing water through the overflow and the toilet will cycle to makeup the lost water. I've also seen cases where the tube to refill the toilet was installed in such a way that it was below the water level and it eventually siphoned water through the fill valve into the overflow drain. The water would siphon down until the toilet ran to makeup for lost water. The most common reason is a bad seal on the flapper valve. Depending on the flapper design, this may be replaceable without disassembling the toilet tank. One last possibility is a failing valve on the toilet. Typically, the reason these fail is from high water pressure. But the symptom will be a high water level, well above where the float should shut it off. You may find the float submerged if this happens.