According to :

You have to consider the fact that motor switching requires far beefier
switch contactors than their ampere requirements alone would suggest.

Relays and switches used for motors _should_ carry "horse power ratings"
in addition to the ampacity ratings.

While a 30A relay _should_ be beefy enough to handle 1/4-1/3 HP at
120 (which'll draw 3-7A steady state, 20A or more on startup),
I personally would prefer to see a HP rating.

I bought a RF controlled AC relay, intended to drive a 1HP dust
collector. It was rated for about 1000W, not enough. So I used
it to control a massive old HP-rated relay I had laying around.
Massive: it's rated at 15HP at 277V. Enclosed it in the case
from a fried PC power supply ;-)

You don't need something that big. Look for relays rated at
15A/1HP or so.

1. Small 10A relays. They click too, but they are much quieter.
However, I don't know if the contacts can stand the inrush current. I
bought 3-pole relays and connected the poles in parallel, so that
gives me 30A in theory. Is this a good idea?

No. Fractional variations in contact resistance will cause drastic
current imbalances, and generally speaking, it buys you little.

2. Mercury relays. These can handle high currents and cost about $25,
but are they quieter than the small relays? Does anybody know?

I'm not familiar with high current mercury relays.

3. Solid-state relays. I am looking at the Carlo Gavazzi models, which
seem very nice. They have models with 24VAC input, and a 50A relay
costs about $30. The voltage drop across the relay is 1.6V, and at
steady state the currents I am dealing with are low enough that I
won't need to install heat sinks.

It's _particularly_ critical with solid state relays to look for
some sort of HP rating or allowance for high surge loads - see the
specs. Semiconductors blow a lot faster than mechanical contactors or
fuses.

Note that running a solid state relay with a DC actuator on a 24VAC
circuit is pretty easy. A small bridge rectifier (a buck or two)
(and perhaps a small electrolytic capacitor) will do the trick. Depends
on how far you want to DIY this. Of course, there are solid state relays
designed for 24V AC control too.
--
Chris Lewis, Una confibula non set est
It's not just anyone who gets a Starship Cruiser class named after them.