First, check to see if the 1620 supports private vlans, or port isolation. Probably not, but check.
Failing that, you have two choices:
1. If your switch supports routing, then each of your client VLANs has its default gateway on its VLAN interface on the switch. You then need another VLAN which will be the point to point link to the router. The switch needs a default route pointing at the router and the router needs routes for each of your internal subnets pointing at the switch
2. You trunk all VLANs to the router and the router has a VLAN or sub interface for each VLAN which has the IP address that is the default GW for each VLAN.
Frankly, I would guess that neither of your devices has the capabilities you require to make this work.