The current communis opinio is both Latin words oleum and oliva were borrowed from Greek, which, in its turn, are of Pre-Greek origin (e.g. Beekes 2009/2016, Ernout & Meillet 2001); cf. Miller 2014 "there are cultural and phonological reasons for thinking Latin borrowed it from Greek" (p. 31).
Miller 2014 writes that
"Since Attic-Ionic lost /w/ prehistorically, Greek words borrowed into Latin with v /w/ are either from a West Greek (Doric) dialect, or possibly early enough to have been Mycenaean loans" (p.31).
Latin oleum < *olēwom < *eleiwom < Gk. *élaiwon (Miller 2014), cf. ἔλαιον
Latin oliva < Gk. *elaíwā (Beekes 2009/2016), cf. ἐλαία
All of the sound changes above are well-known and described in any historical Latin grammar worth reading, e.g. Weiss 2009/2011 (the first book I grabbed from my bookshelves).
- *e > o/_ɫ (p. 139);
- ai > ei > e (> i) (a-weakening, Weiss tells us, precedes monophthongization, p. 120);
- *ei > *ẹ̄ > e (p. 143) etc.
As for a possible Etruscan intermediary hypothesis suggested by TKR (was it borrowed directly from Greek or via Etruscan?), this is highly speculative. As Clackson and Horrocks 2007/2011 write,
"All languages of central Italy participate in borrowing words for material artefacts from Greek. Often we may be unable to tell whether a word came directly from Greek or via the medium of another language: Greek *kulίkʰna 'cup' borrowed as Latin culigna, Etruscan culicna, Oscan culchina/culcfna" (p. 46; emphasis mine — Alex B.).
For more information we will need to look it up in De Simone 1968–1970 and Watmough 1997 — and I will. I encourage you to read these books too!