The Collaborative International Dictionary of English v.0.48:

May \May\ (m[=a]), v. [imp. Might (m[imac]t)] [AS. pres. maeg
   I am able, pret. meahte, mihte; akin to D. mogen, G.
   m["o]gen, OHG. mugan, magan, Icel. mega, Goth. magan, Russ.
   moche. [root]103. Cf. Dismay, Main strength, Might. The
   old imp. mought is obsolete, except as a provincial word.]
   An auxiliary verb qualifying the meaning of another verb, by
   expressing:
   (a) Ability, competency, or possibility; -- now oftener
       expressed by can.
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             How may a man, said he, with idle speech,
             Be won to spoil the castle of his health!
                                                  --Spenser.
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             For what he [the king] may do is of two kinds; what
             he may do as just, and what he may do as possible.
                                                  --Bacon.
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             For of all sad words of tongue or pen
             The saddest are these: "It might have been."
                                                  --Whittier.
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   (b) Liberty; permission; allowance.
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             Thou mayst be no longer steward.     --Luke xvi. 2.
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   (c) Contingency or liability; possibility or probability.
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             Though what he learns he speaks, and may advance
             Some general maxims, or be right by chance. --Pope.
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   (d) Modesty, courtesy, or concession, or a desire to soften a
       question or remark.
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             How old may Phillis be, you ask.     --Prior.
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   (e) Desire or wish, as in prayer, imprecation, benediction,
       and the like. "May you live happily." --Dryden.
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   May be, & It may be, are used as equivalent to
      possibly, perhaps, maybe, by chance,
      peradventure. See 1st Maybe.
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The Collaborative International Dictionary of English v.0.48:

Might \Might\ (m[imac]t),
   imp. of May. [AS. meahte, mihte.]
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The Collaborative International Dictionary of English v.0.48:

Might \Might\, n. [AS. meaht, miht, from the root of magan to be
   able, E. may; akin to D. magt, OS. maht, G. macht, Icel.
   m[=a]ttr, Goth. mahts. [root]103. See May, v.]
   Force or power of any kind, whether of body or mind; energy
   or intensity of purpose, feeling, or action; means or
   resources to effect an object; strength; force; power;
   ability; capacity.
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         What so strong,
         But wanting rest, will also want of might? --Spenser.
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         Thou shalt love the Lord thy God with all thine heart,
         and with all thy soul, and with all thy might. --Deut.
                                                  vi. 5.
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   With might and main. See under 2d Main.
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WordNet (r) 3.0 (2006):

might
    n 1: physical strength [syn: might, mightiness, power]

Moby Thesaurus II by Grady Ward, 1.0:

135 Moby Thesaurus words for "might":
   adequacy, amperage, ampleness, amplitude, arm, armipotence,
   ascendancy, authoritativeness, authority, beef, black power,
   boundlessness, brawn, brute force, bulk, capability, capacity,
   charge, charisma, clout, cogence, cogency, command, competence,
   compulsion, control, decisiveness, dint, domination, dominion,
   drive, duress, effect, effectiveness, effectuality, endurance,
   energy, enormity, enormousness, expanse, flower power, force,
   force majeure, forcefulness, formidableness, fortitude, full blast,
   full force, fullness, gigantism, grandeur, grandness, great scope,
   greatness, guts, gutsiness, hardiness, heartiness, hugeness,
   immensity, infinity, influence, intensity, intestinal fortitude,
   jurisdiction, largeness, lustihood, lustiness, magisterialness,
   magnitude, main force, main strength, mana, mastery,
   might and main, mightiness, moxie, muchness, muscle, muscle power,
   obstinacy, pizzazz, plenitude, poop, potence, potency,
   potentiality, power, power pack, power structure, power struggle,
   powerfulness, prepotency, prodigiousness, productiveness,
   productivity, puissance, pull, punch, push, qualification,
   robustness, ruggedness, sinew, stalwartness, stamina,
   staying power, steam, sticking power, stoutness, strength,
   strength of will, strenuousness, strings, strong arm,
   stupendousness, sturdiness, superiority, superpower, sway, thew,
   toughness, tremendousness, validity, vastness, vehemence, vigor,
   vigorousness, vim, virility, virtue, virulence, vitality, wattage,
   weight