Sunroof leaks faster than drain pipe can empty tray below glass. I assume it due to gasket shrinkage after 14 years. Any known fixes?

Check both drains near the front of the sunroof. I use a small cup and pour water into the drain hole, water should start pouring out immediately if the drains are not clogged. No matter how hard it rains, the drains should handle any water leaking around the SR.

If water pools because the drains are clogged, try some flexible wire to gently push down the drain tubes. Compressed air might also work, but do not force water from a hose down the tube, the tube has a couple of joints that can come apart under high pressure.

Have you had the windshield replaced? My 1998 V70 used to leak and drip water on the passenger side of the dome lights. I found that the problem was the seal at the top of the windshield glass, under the black rubber strip. Careful application of caulk solved the problem.
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My back feels better when I sit in a Volvo seat

Pouring hot, not boiling hot, but pretty darn hot water through the drain holes can help loosen organic material caught in there sometimes. A little Dawn in the water wouldn't hurt either. That is also a good thing to do every year or so to keep them flowing well. The rooter method Klaus described is about your only alternative. If I were having your problem, I'd do both, likely at the same time.

I also heard a story where a guy crushed up some denture cleaning tabs and blew the dust in there with a straw followed by hot water to successfully clean a clogged SR drain. This is total hearsay but if I had 'em laying around it's just the type thing I might try.