Escape, avoid, evade, elude, shun, eschew are comparable when meaning to get away or to keep away from something which one does not wish to incur, endure, or encounter.
Escape when referred to persons (sometimes to animals) usually implies a threat to their liberty or well-being; in this sense it may not imply running away from or even an effort to miss what threatens, but it does suggest the latter’s imminence or likelihood.
When extended to things and especially to inanimate or intangible things escape connotes something comparable to a net which holds and confines yet permits passage through it.
Avoid, in contrast with escape, suggests a keeping clear of what one does not wish to risk or knows to be a source of danger, rather than a getting away from what actually threatens; thus, one may escape suspicion by avoiding persons or places that are being watched; one may avoid all known sources of contagion yet not escape infection.
Avoid, however, is often used interchangeably with escape; it may be preferred when a danger is averted by forethought, prudence, or caution.
Evade implies escape or the intent to escape, but it also commonly suggests avoidance by the use of adroit, ingenious, or, sometimes, underhand means; thus, one evades suspicion who escapes it by spreading rumors that throw others off the scent; one evades a question one does not wish to answer by seeming not to hear it.
Elude comes closer to escape than to avoid but stresses a slippery or baffling quality in the thing which gets away or cannot be captured.
Elude, however, is sometimes used in place of evade when there is a strong suggestion of shiftiness or unreliability or of the use of stratagems.
Shun differs from avoid chiefly in its added implication of an abhorrence or aversion that is sometimes temperamental in its origin but oftentimes rational and dictated by conscience, experience, or sense of prudence.
Eschew comes very close to shun in meaning but tends to stress practical, moral, or prudential rather than temperamental reasons for the avoidance.