This is actually a pretty complicated topic.
The change in the pronunciation of the vowels can be considered a secondary effect of the change in stress. Changing the pronunciation of a vowel in an unstressed syllable is called "vowel reduction". In "telepath", the first syllable is stressed, so the vowel is pronounced as unreduced /ɛ/, whereas in "telepathy", the first syllable is unstressed, so the vowel is reduced to schwa /ə/.
In stressed syllables, single vowel letters can usually be pronounced at least two ways in English (one of the most notorious features of its spelling) but a complete account of the rules for vowel pronunciation in stressed syllables based on the context would be rather long and I don't think the examples really call for it. So the rest of this answer will just be about stress patterns.
In sociopathy, telepathy and biography, the stress is on the third-to-last or "antepenultimate" syllable. This is actually a fairly common position for stress in Latinate words, and "sociopathy" and "telepathy" belong to a particular subtype of words where this stress shift is common: compounds of Greek roots ending in -y, where the second element ends in a single consonant. I know that explanation is a bit complicated, so here are a few examples: geology, geography, astronomy and in general words ending in -logy, -graphy, -nomy, -phony, -scopy.
Anther noun ending that causes stress to fall on the antepenult syllable is -ity.
However, I don't know enough phonological theory to explain why this stress pattern is used in these words.
Athletic, episodic and biographic are examples of a rule that adjectives ending in the suffix -ic are stressed on the second-to-last syllable (with some exceptions).
Some people have tried to explain the -ic stress rule as resulting from the application of the third-to-last rule by using certain abstract analyses of the structure of words, but I haven't yet seen an explanation along these lines that seemed convincing to me. (For example, Chomsky and Halle's The Sound Pattern of English (1968) argued that "-ic" words with stress on the second-to-last syllable have an underlying form with an extra syllable "al" that has been deleted; this is not entirely unmotivated as "ic" words do often coexist with "ical" words with "al" explicitly present, and there is a spelling rule by which adjectives ending in "ic" usually correspond to adverbs ending in "ically", but nevertheless it seems rather far-fetched. This analysis is mentioned by Erik Fudge in "English Word Stress: Basic Assumptions", a paper in Essays on the Sound Pattern of English (1975), edited by Didier L. Goyvaerts and Geoffrey K. Pullum. A different explanation given by Jonathan B. Alcántara in "The Architecture of the English Lexicon" (1998) is that words like "athletic" and "episodic" actually end in a segment /ə/ that "is never allowed to surface, but will provide a final syllable" that explains the stress pattern of these words (3-114). In other words, the suffix spelled "ic" is in some way really /-icə/.)
There are other monosyllabic suffixes that behave similarly to -ic, such as the adjective suffix -id, the verb suffix -ish, and the noun suffix -ule. It has been observed that these (and also the disyllabic suffixes that commonly trigger trisyllabic shortening, like -ity, -ify, -ular, -ual, and according to Alcántara -ible, although I'm unsure if this suffix is actually a very consistent trigger of a short vowel in the preceding syllable) all start with high vowels (Alcántara A-310), but I'm not sure if this is significant in the way it might be taken to be; these endings are from Latin endings that contained short vowels (e.g. -ĭcus, -ĭdus, -ŭlus, -ĭtās, -ĭfĭcāre, -ĭbĭlis, -ŭlāris, -ŭālis) and non-high short vowels had a somewhat limited distribution in word-internal (not initial or final) open syllables in Latin due to processes of vowel reduction that turned other vowels into ĭ and ŭ in these contexts.