You are quite right--they are very uncommon, college-level words (though I've usually already encountered about a third of them since I am well-read). Here are the definitions:
fervid - heated and very passionate
protege - basically a student
prolix - wordy
prototype - original model
ecumenical - something that is...sort of constantly present and widespread, usually refers to a product or disease, but I had to be creative.
heyday - period of greatest power
tautology - study of a certain idea
sycophant - someone who flatters other people
inveigle - to persuade using flattery/bribery/the like
kudos - congratulations, compliments
lagniappes - extra gifts, usually refers to complimentary products, I think, but I had to be creative.
fetid - sort of the adjective form of "reek"
truckle - follow with a resigned air
gargantuan - massive
incubus - a daemon that gets you in the middle of the night
infrastructure - basic structure/foundation
bete noire - something which is particularly distasteful or unbearable
bode - implying something that will happen, foreshadowing for example
beautitude - state of extreme happiness or bliss
* utopia = Greek for "no place". A bit of a joke on Sir Thomas More's part.
Those are as precise as I can get, since I wrote the essay with no sleep, and I'm sure I don't remember the exact definitions. Remember, however, that the "definition" of a word pales in comparison to connotation--in order to truly know the English language, one must have a "feel", so to say, for words. Dictionary definitions cannot possibly suffice.
That is why you must, above all, read, because if you don't gather the context clues to know how a word feels three-dimensionally, you're going to cripple yourself and spend your life saying things in awkward half-Chinese/English.
(I apologize, I am particularly angry with, especially, classmates of mine who don't even bother to understand the meaning behind words, much less feel them, and they have the opportunity to truly know this language. Plus I'm cranky from lack of sleep.)
Since it is a particular pet peeve of mine to define words for people (even though I know I said I would), I would like to point out a fantastic resource for you:
www.dictionary.com
Merriam-Webster's dictionary of the English language. It will help you understand the above words better, but remember that the best way to learn them is to encounter them in literature.
Ironically, words like that are only found in Hamlet, Jude the Obscure, and lectures on La Commedia Divina, classical silliness that only I seem to bother to read.
Jake