On an east-west airway, when would I hold north of the airway, and when would I hold south of the airway and why?

Mildred's people

An airway's direction has nothing to do with how a published holding pattern might be associated with it. The holding pattern will either be the airway itself as the inbound leg, or be another radial to another RNAV or radio fix, such as the IAF of an instrument approach. The orientation and direction of the hold will either be published or instructed by ATC. The position of the hold (n,s,e,w, nw, etc) with respect to the holding fix is usually a matter of putting it in the safest quadrant... one that's not encroaching Restricted airspace, air traffic flow, obstructions, etc.

lowlevel

Neither unless specifically directed by ATC. You hold ON the airway at a specific fix or DME or published hold.. right hand turns unless published or cleared otherwise.

Big Mike

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USAFisnumber1

Two factors. First is wind direction, second is the flight pattern used at the airport.

JetDoc

You will hold where and when the ATC tells you to.