Abarim Publications' online Biblical Greek Dictionary
The form ου may either be a particle of negation (meaning "no/not"), or an adverb of place (meaning "there"; see below), or the genitive singular masculine or neuter of the relative pronoun ("that/who/which"). Accents make clear which word is used but when the Bible was written these accents weren't used yet, and the interpretation is up to the reader's good humor. Then there are some expletives which have similar forms (meaning something like "O no!"; see below), and may derive or be perceived to derive from either.
The particle ου (ou) — spelled ουκ (ouk) when the next letter is a vowel — is one of two common particles of negation; the other one is μη (me) and both happen all over the New Testament. The difference between the two is that ου (ou) describes an objective negation and μη (me) a subjective one. The difference there is that a subjective negation says no to one of multiple options while an objective one disregards those. A subjective negation has to do with condition, supposition or even aspiration, and is often part of constructions like "may it not happen" or "if not/ would not". Our particle ου (ou), on the other hand, describes an absolute and blunt non-existence without further review of alternatives — NO! — the opposite is ναι (nai), meaning yes (Matthew 5:37).
On occasion, these two particles of negation occur side by side, as μη ου (me ou), an interrogative expression (Romans 10:18, 1 Corinthians 9:4). But, in the eloquence of Spiros Zodhiates, "in this combination, me is interrogative and the ou belongs solely to the verb following" (Complete Wordstudy Dictionary). Note that while our modern Boolean sense of negation dictates that two negatives create one positive (not-no means yes), in Greek a double negation emphasizes it (no-no means absolutely not).
Our word occurs 1641 times, see full concordance, and comes with a small list of derivatives (many of which also exist formed from μη, me instead):
- Together with the particle δε (de), which usually merely indicates a mild transition and is rarely translated: the conjunction ουδε (oude), meaning something like "and not" or "neither" as this word often follows a previous negation. It's used 136 times, see full concordance, and from this word in turn derives:
- Together with an otherwise unknown word αμος (amos), which appears to have meant way or wise: the adverb ουδαμως (oudamos), meaning in no wise, by no means (Matthew 2:6 only).
- Together with the adverb ποτε (pote), meaning whenever: the adverb ουδεποτε (oudepote), meaning not yet ever or never yet. This word is used 16 times; see full concordance.
- Together with the particle πω (po), meaning yet or even: the adverb ουδεπω (oudepo), meaning not yet or never yet. This word occurs 5 times; see full concordance.
- Together with εις (heis), the cardinal number one: the adjective ουδεις (oudeis), meaning not even one; nothing or no one. This word appears 235 times; see full concordance.
- Together with the adverb ετι (eti), meaning still or yet: the adverb ουκετι (ouketi), meaning no longer, no further, not anymore. This word occurs 48 times; see full concordance.
- Together with the conjunction ουν (oun), meaning accordingly or certainly (see below): the adverb ουκουν (oukoun), which is used as an adverb of confirmed inquire, meaning "isn't it so?" and implying that it is, indeed, so. This word occurs only in John 18:37.
- Again together with the particle πω (po), meaning yet or even: the adverb ουπω (oupo), meaning not yet or not even yet. This word is used 23 times; see full concordance.
- Together with the conjunctive particle τε (te), meaning and: the conjunction ουτε (oute), meaning neither, and not, also not, etcetera. This word is used 92 times; see full concordance.
- The adverb ουχι (ouchi), which is an emphasized version of ου (ou), and would mean certainly not, or not at all (Romans 3:27, 1 Corinthians 6:1). Often it's used in an interrogative context, in which case it means "is it not?" and implies that it surely is! This word occurs 56 times; see full concordance.
Spelled identically to the particle of negation and the genitive singular relative pronoun, the adverb ου (hou) is an adverb of place and means where (Luke 4:16, Romans 4:15, Colossians 3:1). Sometimes these identical forms pose a bit of a challenge. In Matthew 18:20, for instance, Jesus begins his famous declaration of his presence among two or more, with ου γαρ, which technically may mean that he won't be in their midst, instead of there he would be (the same ου γαρ combination means precisely that in Matthew 9:13, 9:24, 10:20, and so on). Fortunately, early interpreters have long concluded that the former option agrees more with Jesus' character than the second. This word occurs 27 times; see full concordance.
Somewhat in the same ballpark is the conjunction ουν (oun), which ties two subsequential clauses together, whether they merely happen to come one after the other or whether the second one logically follows from the first. It mostly means therefore, there upon, certainly, and then, etcetera.
Our word ουν (oun) looks like the particle of negation ου (ou), suffixed with a ν (n) and given an affirmative meaning. Note that the particle of strong affirmation μην (men) looks like the other particle of negation μη (me) followed by an ν (n). Our word ουν (oun) occurs 523 times; see full concordance.
The interjection ουα (oua) expresses admiration or astonishment, and ουαι (ouai) expresses pain or anger. These words (if that predicate becomes them) are relatively rare in the classics but not so in the New Testament.
They are probably onomatopoeic — that is: the spelled out versions of the sound someone makes when informally expressing disgust, indignation or grief — but their similarity to the particle of negation ου (ou) is obvious. Or said elsewise: these interjections sound as much like "Aye!" as like "No!".
For lack of a suitable alternative, particularly ουαι (ouai) is most commonly translated with a rather archaic "woe". It is used 47 times; see full concordance. The shortened form ουα (oua) only occurs in Mark 15:29.