You need to configure your Squid box to be transparent.
Since you already have a working Squid configuration, all you need to do is follow steps 4 & 5 from this article:
Transparent Proxy With Squid
...but this is assuming 2 things:
1.) Your Squid box is on the default gateway itself...if not; if your Squid box is on a DMZ, then follow steps 4 & 6 instead.
2.) You are using iptables on the default gateway
You might also wish to configure the default gateway to block all OUTGOING requests on port 8080 and port 3128...this way, you users can't cheat and use an external proxy.