Short answer: NYOO-sis, or if you’re American, NOO-sis.
As there are multiple traditions for pronouncing Ancient Greek words, and words derived from ancient Greek, nobody can give you a single “correct” answer. There are always people who have the misimpression that whatever they learned in their Greek class, either reconstructed pronunciation or modern Greek pronunciation, is the One True Way to pronounce the word, and anything else is a corruption, but we can easily see from countless examples such as “psychology,” “schizophrenia,” and “Logos” that there is no one system for determining how English speakers pronounce words from Ancient Greek. We certainly don't pronounce them the same as the Ancient Greeks, the Modern Greeks, or the Germans in most cases.
However, the major system people use in disciplines like mathematics, science, medicine and law is the traditional Anglicized pronunciation (although this PDF is about medical terminology, it provides a good overview and the rules are the same).
Your analogy with words like “neurology” is in fact sound: in essentially all cases, words that in Greek had the diphthong ευ, transliterated as eu, are pronounced in an English-language context with exactly the same sound as the digraph “eu/ew” that appears in normal English words: that is, a “long u” sound, "yoo," or IPA /juː/. In most American dialects this sound has gone through an additional change under certain conditions following an n to become an “oo” sound, IPA /uː/ (a parallel example is the word "new").
"OY" (more or less) is the Modern German pronunciation of the digraph "eu", in both native German words (like neu "new") and words from Greek, but there's no obvious reason for basing the English pronunciation of "neusis" on German, as there is for the name "Euler", which is German. (We don't pronounce the name "Euclid", from Greek, as "OY-clid"; the Germans do, but they spell the name "Euklid".)
I don't know Greek, but my understanding is that the word νεῦσις would be pronounced /ˈne̞fsis/ in Modern Greek. This is generally supposed to be a development from an earlier pronunciation with a diphthong, like /ˈneu̯sis/, but the exact reconstruction of the older pronunciation, the timing of the transition from a diphthong to a vowel-consonant sequence, and any intermediate steps are all debatable (even ignoring the outright cranks—unfortunately all to easy to encounter—who insist that Greek has always been pronounced with almost exactly the modern Greek pronunciation for as long as it has been written). If you're interested in learning more about the pronunciation of historical Greek, you may want to sign up for the Greek Language SE proposal, or (if the question is about Classical Greek) ask at the currently existing Latin SE. (A similar question about the evolution of the pronunciation of β already exists.)