I have 3 VLANS configured on a single vSwitch in the ESXi host. That vSwitch is using two NICs (nic1/nic3). How do I configure the Cisco ports and the NIC Teaming under the vswitch to pass tagged and untagged traffic? I have tried to set up port-channels and configure the ports for trunking, but as soon as i do, I lose connectivity to the ESX server.
Since you are NIC teaming on the server you need to do portchannel with LACP on the switch site. Then configure the physical and portchannel as trunks.
ESX does not support LACP. You will need to configure your portchannel to "mode on". Here is a extensive document that may help you in setting up the switch.