This is not an issue that can be fixed in the 'rsyslog' configuration - this is a TCP routing issue (layer 3 networking). All you can do with 'rsyslog' is give it a specific hostname or IP address to send traffic to; exactly how that traffic is sent is up to the system's network configuration.

That said, it shouldn't be too hard to force the outgoing rsyslog traffic to go via the eth0 interface (as long as the network is set up to allow that - there must be a gateway (router) device on the subnet which is attached to eth0). I can't test this (don't have a triple-homed host), so please check "man ip-route" or "ip route help" for the details...but something like this should work:

ip route add (IP-of-remote-syslog-host)/32 via (IP-of-gateway-on-eth0)

(you may also have to add a "weight" parameter to force a higher priority than other routes defined on the system).

Be careful with this sort of configuration; it can lead to asymmetric routes, which can cause problems with firewalls. You might have to set an equivalent rule on the syslog host to make sure return traffic goes via the same path. Not to mention the general confusion among sysadmin and network admin staff caused by per-host unique routes.