Speedbird,
You are outside controlled airspace, so you can fly wherever you like. The airway a few hundred feet above you shouldn't affect your flight at all.
There are two times you need to fly at right angles to an airway, and they both relate to VFR flight (i.e. not relevant to your IFR flight). The first is to cross the base of an airway. If N864 starts at FL55, and you are VFR at FL55, you may cross the airway at right angles. (This rule seems a little silly to me - surely much easier to fly at 5400 on 1013mb and not worry about the airway? But that's the rule, anyway.)
The second time you must fly at right angles to the airway is if you are flying in VMC and you want to fly through the airway (e.g. in the case of N864 at FL65). To do this, though you need to file a flight-plan (you can do this in flight) and request permission. More importantly, though, you must have a valid Instrument Rating.
IFR in IMC, neither of these options is available to you, so you can safely ignore them. Enjoy your flight!
FFF
-------------