Can static electricity affect navigational instruments?
This will depend on the system, but the over all answer would be Yes at least to some extent. When talking about VOR/VORTAC/DME/NDB/GPS or any other nav system that relies on both a device in the plane as well as a device elsewhere we must consider how these devices talk. In this case we are talking about radio waves (em propagation), and lighting does produce an EM field so it has the capability to interfere. 

That being said "interference" has both a technical term and a reality IMO. On paper, yes this may interfere with the signal but in reality lightning is fast and isolated so its momentary interference may not interfere with the operation of the device over a usable amount of time or may cause a momentary drop out. 

Local INS (Inertial Navigation Systems) if you have it would remain generally unaffected.

There is another issue that presents itself if the lighting is very very close to the aircraft and will be more of an issue with composite aircraft. For what it's worth, if the whole skin of an airplane is conductive (as with metal skinned aircraft) it will act as a pretty solid Faraday cage. This will vary from plane to plane but is generally true. Thus if the lightning generates a strong enough EM pulse the interior of the plane will be protected from it. On a composite based plane you potentially expose yourself to flux related power surging. It should be noted that the critical electronics are protected from this kind of damage.