The formation of adjectives from names is sometimes (although not always) based on etymology. When not based on etymology, analogy with other adjectives can play a role. As Greg Lee mentioned, there are no firm principles about the formation of such adjectives.
Adjectives ending in ian, -eian, -ean tend to come from Latin adjectives ending in -ius, -eius, -eus, which in turn may come from Greek adjectives ending in -ιος or -ειος.
Ancient Greek seems to have an adjective Ὀδύσσειος which can anglicized as Odysseian, Odyssean or Odyssian. Because Greek ει was Romanized in multiple ways, it can correspond to any of ei, e or i in an English word: there is no strict rule about which form is "correct". The Google Ngram Viewer seems to show that the spelling with -ean is more common.
The use of -yan vs. -ian
In English, final -y tends to be a contextual replacement for the letter -i. When that is the case, related words are usually spelled with i in non-final contexts, unless there is a preceding vowel letter. There are alternations not only with latinate suffixed forms (like territorial vs. territory, or colonial vs. colony), but also with English inflected forms such as bellies from belly or bloodied from bloody.
When there is a preceding vowel letter, it is regular for the spelling with y to be retained in English inflected forms: saying, keys. In latinate suffixed forms, the spelling is not very predictable. Depending on the etymology of the word or name, a related adjective could end in -ian, yan, or even -jan (Troy, Trojan). The spelling Tolstoian might be partially based on the alternative romanization Tolstoi.
However, the name Shelley is not romanized, but the OED says that a spelling variant Shelleian exists aloongside Shelleyan. Likewise, both Bradleian and Bradleyan seem to be used as adjectives from the name Bradley. And on the other hand, some names ending in a consonant and -y have adjectives that can be spelled with -yan; e.g. Chomskyan exists alongside Chomskian. So I'm not sure that there's any definite rule about when to use -yan vs. -ian in the spelling of such words.
The use of -vian
V is a Latinization of a [w]-like sound. It occurs in some ian adjectives when the preceding vowel sounds something like [u] (e.g. Peru, Peruvian) or [o], or when the vowel just has a spelling with w (as with the digraph aw, e.g. Shaw > Shavian).
Foucauldian is very strangely formed. Apparently, the Dictionary of American Family Names says the last part of the name Foucault is from an element wald "rule" (Ancestry.com); I wonder whether that has something to do with the d spelling of the related adjective. Foucaultian does also seem to have some usage. I found a mailing list discussion where a user suggested the form Foucauldian is used for "euphonic" reasons, which doesn't make that much sense to me: there are many English words with t in the middle. It's true though that it is not usual for a word to end in -ltian specifically. A Google search reveals that a few people have used Rooseveldian instead of Rooseveltian, which seems similar.
Rimbaud has the adjective Rimbaldian, which doesn't have the t to d change but which ends in the same -ldian sequence.