No particular arguments with Michael (was it - you can't see other answers when you do this!!)

Handicapped & disabled are largely synonynous, and it can be either mental or physical, congenital or something that has developped/happened. Both terms cover most things

Invalid would usually imply a disability resulting from injury, e.g. war invalids. And would be physical not mental, and permanent or at least very long term

Incapacitated - also physical, usually. Usually temporary by implication, although possibly long-lasting. Also implication that the "condition" only precludes certain activities, and does not affect "life in general", e.g. incapacitated for work (such as a translator with both hands in plaster!)

Please check the following links from an encyclopedia:

www.thefreedictionary.com/disabled
www.the freedictionary.com/invalid
www.thefreedictionary.com/incapacitated
www.the freedictionary.com/severely+disabled
wwww.thefreedictionary.com/handicapped

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Note added at 1 hr 45 mins (2005-04-11 21:44:12 GMT)
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www.thefreedictionary.com/invalid
www.thefreedictionary.com/severely disabled

I predict you'll get a lot of feedback on this question, as so much of this language is under siege from "linguistically/politically correct" hypersensibilities ... but here goes:

DISABLED/HANDICAPPED are more or less synonymous, are used as adjectives or adjectival nouns ("the disabled") to describe people primarily with physical disabilities. In particular, these words designate those who qualify for special protection under the law or benefits from the state. People will argue over which one of these two words is currently "in fashion," but fashion is all it is; they mean the same thing and are both currently in wide use.

INVALID in this context is used only as a noun; an invalid is someone who is wounded (as in war) or handicapped.

SEVERELY DISABLED is the augmentation of disabled, e.g. someone who is partially or wholly paralyzed.

INCAPACITATED means hindered and is often used to describe a temporary state.

I speak from a perspective of US-EN; I'll let any Brits who may be online at this hour add whatever distinctions are relevant for UK-EN.

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Note added at 18 hrs 23 mins (2005-04-12 14:21:34 GMT)
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A basic problem with such language is the misunderstanding of what distinguishes a pejorative from a word that simply describes an unpleasant reality. \"Retarded\" and \"crippled,\" for example, were never pejorative, but they are hardly ever uttered any more because they are deemed too harsh. In time, \"special needs\" and \"disabled\" will sound similarly harsh, and the linguistic carousel will spin anew. Ironically, it\'s not the disabled themselves who care about these distinctions (they\'ve got more pressing concerns!) but their (admittedly well-meaning) fully abled advocates. The approach of saying \"people with disabilities\" rather than \"the disabled,\" so as not to define people wholly by their condition, is not w/o merit, but to apply it without exception simply makes for ungainly writing. If fully abled people learn to be as comfortable talking about disabilities as the disabled themselves, this problem would disappear.