Ronald,
IF the host VLAN is int the same VLAN that 192.168.0.X, you should be able to ping the gateway and the rest of the world.
Clients on other VLANs will need to SWITCH to the core router and the go to the world.
IF the clients are in the same subnet as the switch, you should be able to ping the switch, GW, & world.
Verify with show host vlan and show port vlan and also verify egress list of ports (untagged vlan as PVID and tagged all others(uplinks))