Suppose I have Hoth Operations out (and more Hoth objectives than my opponent), and I have 2 speeders on the board. My opponent has Virago and 2 free Scum resources (on different cards). Can he focus those resources to steal Edge (1) from each of my speeders and therefore giving Virago Edge (2) for that phase?

Yep, that works.

I got a reply from Erik Dahlman:

Yes.

With a single copy of Hoth Operations in play (and active), each Speeder you control has "edge (1)." There is no limit to the number of times you can trigger the Virago 's action other than having the resources to pay the cost. As such, your opponent can steal "edge (1)" from each of your Speeders for the phase.

(Also worth noting that, with only a single copy of Hoth Operations on the table, he can only steal "edge (1)" a single time from each Speeder (as they only have one instance of "edge (1)" each.)

Then I asked what would happen if I had 2 Hoth Operations out. Here's his reply:

If you have 2 Hoth Operations out, each Speeder you control now has two copies of "edge (1)" which add together to give you an *effective* edge (2). However , and this is important, they still only have two instances of "edge (1)."

To steal all of them, your opponent would need 4 freem {SCUM} resources; to steal each and every instance of "edge(1)" your Speeders had.