GFCI in garage keeps tripping when I turn on kitchen lights

Some surge protectors work by "redirecting" surges to the equipment ground, which is pretty much the definition of a ground fault. In this case, it's definitely possible that surge suppressors could be tripping GFCI receptacles/breakers (given a large enough surge).

As for the AFCIs... When electrical contacts separate, they often create an arc between the contacts. This arc spans the gap until the contacts are too far apart, and the arc can no longer be sustained. It's possible (in theory) that the GFCI tripping could create a large enough arc, for long enough to cause the AFCI to trip. It's not likely that a properly functioning GFCI would do this, but if the GFCI was old and worn it could be opening the contacts slow enough that a detectable arc is being produced.

Determining if the GFCI tripping is causing the AFCI to trip, is a simple test. Simply press the test button on the GFCI. If the AFCI trips, you'll have figured out half the problem. If the ACFI does not trip, you could repeat the test using a receptacle tester with a GFCI test function.

If it's determined that the GFCI is causing the AFCI breaker to trip, replacing the GFCI receptacle may resolve that part of the issue.

Figuring out if the surge suppressor is tripping the GFCI, is a more difficult proposition. It will likely require you to monitor the supply voltage over some time, to identify and document possible surges.

It certainly seems like you have a ground fault somewhere. Is it possible there is water damage anywhere inside the garage?

Since you've already replaced the GFCI, I think it's safe to assume it's working properly and is tripping as it's designed to. That means somewhere current from the hot or neutral wires is leaking to the ground wire or somewhere else. (I'm guessing it's a neutral -> ground short, since it only happens when you try to use an appliance. A hot -> ground short should trip the GFCI as soon as the power comes on.)

Here are the things I would try:

• Does the tripping happen at the GFCI, or just the downstream outlets? If it's easy to tell which order the receptacles are wired in, start by plugging something in to the first one downstream of the GFCI. Does that trip it? If so, the short is probably between that outlet and the GFCI. If it doesn't trip, move to the next outlet and see if that trips, etc.
• Take the cover off all the outlets and inspect them. Look for any signs of moisture, or a loose wire nut, or a conductor touching the side of the box.
• If you don't see anything suspicious, start pulling the outlets out and rewiring them. Disconnect them all and start adding them back one by one.
• If you still haven't found the issue, it's possible the wiring inside the wall got damaged somehow. Possibly a combination of mice chewing on the wires and moisture from the storm? If you've reconnected the wiring to the outlets one by one, starting with the closets, you should at least be able to tell which section of wall the defect is likely to be in.

Other notes:

• I'm not sure if the continuity tester will help much, the problem is a short not an open circuit. Especially if the problem is caused by a neutral / ground short, those are always going to test as continuous since they connect at the main breaker box.
• I wouldn't worry too much about the voltage readings you got with the GFCI tripped, open circuits can sometimes have small but non-zero voltage readings.