Let's Skype, Skype me

Very common for me.

Have you heard anyone use any other word for voip calling?

That just reflects the fact that you probably don't operate in a workplace where it isn't clear what mode of communication is meant when someone sets up a "call." At my multinational, explicitness is requisite since the requester could mean POTS-to-POTS (legacy PBXes), VOIP-to-POTS (Nortel softphone for the VOIP, connecting to older PBXes), VOIP-to-VOIP (Asterisk), Skype-to-Skype, or Skype-to-Voice (via VoSky).

When someone says "let's Skype" in my world, they either mean Skype-to-Skype (which is implicit if they are in your Skype contacts) or Skype-to-VOIP using one of our VoSky appliances that's tied into our PBXes. The verb "to call" is almost meaningless these days.

You obviously don't watch Oprah.

My wife does. Oprah's been skyping in and out of viewer homes for months.