iRule to host multiple site redirects on one VIP

Of course you can do it with BigIP.

I'm not sure if you want to forward (like a reverse proxy) or to redirect (301 / 302 responses)

you can do it with irules or Local traffic policies. The easiest solution is local traffic policy (only 302 redirect are available in policies, 301 is available in irules only).

It's a ordered rule base policy with conditions and actions