before vowels om-, word-forming element meaning "raw, unripe," from Greek ōmos "raw," from PIE root *hemo- "raw, sharp-tasting" (source also of Sanskrit amah "raw, uncooked, unripe," Armenian hum; Old Irish om, Welsh of).

word-forming element meaning "bulk, mass," used from 19c., especially in medical use, "tumor," from Latinized form of Greek ogkos (pronounced "onkos") "bulk, size, mass, weight, swelling," in Modern Greek "tumor," a word of uncertain origin.

before vowels oneir-, word-forming element meaning "of or pertaining to a dream or dreams," from Greek oneiros "a dream," a word of uncertain origin, perhaps related to Armenian anurj, Albanian (Gheg) âdërrë.

word-forming element meaning "a being, individual; being, existence," from stem of Greek on (genitive ontos) "being," neuter present participle of einai "to be" (from PIE root *es- "to be").

word-forming element meaning "egg, eggs," from Greek ōon "egg," cognate with Latin ovum, Old Norse egg, from PIE *ōwyo‑, *ōyyo‑ "egg," which perhaps is a derivative of the root *awi- "bird."

before vowels ophi-, word-forming element meaning "a snake, serpent," from Greek ophio-, combining form of ophis "serpent, a snake," probably from PIE *egwhi- (source also of Sanskrit ahi-, Avestan aži- "snake," and perhaps the first element of a Germanic word for "lizard," i.e. Old High German egi-dehsa). Hence ophiolatry "serpent-worship" (1862), and the 2c. sect of the Ophitæ, who revered the serpent as the symbol of divine wisdom. 

before vowels ophthalm-, word-forming element meaning "eye," mostly in plural, "the eyes," from Greek ophthalmos "eye," originally "the seeing," a word of uncertain origin. Perhaps from ōps "eye" (from PIE root *okw- "to see") + a form related to thalamos "inner room, chamber" (see thalamus), giving the whole a sense of "eye and eye socket," but Beekes rejects all this and finds it to be probably Pre-Greek.

before vowels ornith-, word-forming element meaning "bird, birds," from combining form of Greek ornis (genitive ornithos) "a bird" (in Attic generally "domestic fowl"), which often was added to the specific name of the type of bird, from PIE *or- "large bird" (see erne).