Awry, askew, askance mean deviating from a straight line or direction. They may all imply divergence from what is straight or straightforward, direct, symmetrical, or orderly, but they are seldom applicable to the same things.
Awry carries a strong implication of disorderliness, of disarrangement, or of confusion.
Askew stresses crookedness or distortion. It implies that the thing so described is set at a wrong angle, is twisted out of its proper position, or goes off in the wrong direction.
Askance is used chiefly in the set phrases “to look, or eye, or view askance” which all mean to observe or examine with mistrust, suspicion, disfavor, jealousy, or disapproval.