Lewis & Short

1. O, o, the fourteenth letter of the Latin alphabet, corresponding to the Gr. ο and ω. The Latin language possessed both the sound and the sign from the earliest times; whereas the Etruscan language never possessed the o, and the Umbrian seems not to have received it as an alphabetical character till a later period. The oldest monuments of the Latin tongue frequently employ o where the classic language has u. So on the Column. Rostr. MACESTRATOS (acc. plur.), EXFOCIONT, CONSOL, PRIMOS (nom. sing.), CAPTOM; in the epitaphs of the Scipios, HONC OINO, COSENTIONT, DVONORO OPTVMO VIRO (bonorum optumum virum); in the S. C. de Bacch. IN OQVOLTOD al. And even in the later inscrr. and MSS., we sometimes find o for u: POPLICO, POPOLVM, TABOLEIS, in the Tab. Bantina: FACIONDAM DEDERONT, Inscr. Orell. 1585: MONDO, HOC TOMOLO, ib. 4858: fondus, fornacatibus, solitodo, etc., in good MSS. (v. Freund, Cic. Mil. p. 18). And, on the contrary, u for o in the old forms, fruns, funtes, for frons, fontes, v. h. vv.: RVBVSTIS for robustis, in the Cenot. Pisan.; v. Inscr. Orell. 642: NVMENCLATOR, Inscr. Grut. 630, 5: CONSVBRINVS, ib. 1107, 1: SACERDVS, ib. 34, 5: VNV LOCV, ib. 840, 1. O appears in class. Lat. particularly in connection with qu and v: quom, avos. This interchange of o and u seems to have been effected rather by dialectical and local than by organic and historical causes; just as in the modern Italian dialects a preference is shown on the one hand for o and on the other for u, and in one and the same dialect the Latin o has passed over into u and the u into o.
On the commutation of o and e, see the letter E.
We have o for au in Clodius, plodo, plostrum, sodes, etc. (also in polulum for paululum, Cato, R. R. 10, 2).
O inserted in the archaic forms: Patricoles, Hercoles, v. Ritschl ap. Rhein. Mus. 8, p. 475 sq., and 9, p. 480. As an abbreviation, O. stands for omnis and optimus: I. O. M., Jovi Optimo Maximo: O. E. B. Q. C., ossa ejus bene quiescant condita, Inscr. Orell. 4489; cf.: O. I. B. Q., ossa illius bene quiescant, ib. 4483; 4490: O. N. F., omnium nomine faciundae, ib. 4415: O. T. B. Q., ossa tua bene quiescant: O. V., optimo viro, ib. 4135; also: optimi viri, ib. 5037.