fast but not easy solution is to run PPPoE server and to make changes all clients to move over this service.
Bad - have to go to all clients if they don't know how and what to set up… and believe me they don't.
If you using DHCP, then create leases and give static IP's to all users. Create MAC filter in the router. Scan who send more than 10 ARP requests per second and lock it. (Better make new scope for IP's where you don't have any users and start it.)
Segmenting the network is the only good, cheap and long term reasonable idea. Fastest way is to put few old WRT's with OpenWRT or DD-WRT. They support VLAN-taging, MAC filtering, port managing (ugh - but don't really support Layer 3 filtering).
Next step is using L3 switches.