Using a relay for retro clicky sound - how do I make it louder?
Try using an inexpensive power relay such as the T90 series, and attach it to a resonator board which will act like the cone of a speaker. They draw about 1W each.

Since you're after an aesthetic effect you'll have to fiddle with it, I think. 



Now if you really want buzzy clanky sounds, you can consider an AC powered "definite purpose contactor" as used in HVAC equipment which will be very noisy and retro sounding. They are not even that consistent in their sound (because of the AC power), which I suspect is useful in your application because they don't sound like a fake synthetic sound. You'll need something like an SSR or a small relay to control the contactor. They're huge and don't mount on PCBs. 

You can get a similar effect (at less sound level) by feeding the DC relays with some kind of randomized power (such as a ramped sine or triangle wave started with random phase) to make them pull in less consistently. Again, you'll probably have to fiddle with it. You can consider the relay as a special kind of speaker with a really weird response (once they pull in and the magnetic circuit is closed the current has to be backed off  a lot for anything much to happen). You could use the contacts to feed back the armature state to a micro. Use something related to your mains frequency such as 120Hz or 50Hz to get authentic mmm..buzz-click sounds. Lots of fun possibilities.