I need to connect two routers via wireless. The actiontec mi424wr (and westell 6100 modem) on one end and the asus wl500g on the other.

here is what I have

(modem)
6100 -> 192.168.1.1, dhcp enabled, 192.168.1.20-30

(router 1)
mi424wr -> 192.168.1.19, dchp relay

---- wireless link ----

(router 2)
wl500g -> 192.168.1.18, dhcp disabled

(workstation)

Is it possible?

If you can tell the background need I think we can help you better.
If you are doing this because you want to increase the wireless signal at your place, you can put the second AP
in repeater mode which can do this.
As far as your question goes, yes it is possible. It must work right away.

I just wanted to use the routers i have accumulated over the years just kicking around to avoid running a wire (damned near impossible), or buying yet more hardware.

It's not about signal strength, I have the signal fine. Basically I have a bunch of equipment on a wired LAN in one room (workstation, printer, etc), and want to connect this LAN to the LAN where my dsl service is in another room on another floor of the building.

Seems like this would be a common use case for wireless router. ?

The problem I find with using in WAP mode is that the router wants a wired connection on its WAN port. Instead I want to use the wireless receiver as the WAN port on the second router.

I didn't see the words repeater in the config screens anywhere on either device... It's doubtfull that I missed it, but it may be called something else?

In scouring the web my biggest hope was WDS. The wl500g has WDS mode. The actiontec does not.