oratorical adj.

late 14c., oratour, "an eloquent or skilled speaker; one who pleads or argues for a cause," from Anglo-French oratour (Modern French orateur) and directly from Latin orator "speaker," from ōrare "to speak, speak before a court or assembly, pray to, plead."

This is sometimes said to be  from PIE root *or- "to pronounce a ritual formula" (source also of Sanskrit aryanti "they praise," Homeric Greek are, Attic ara "prayer," Hittite ariya- "to ask the oracle," aruwai- "to revere, worship").  But according to de Vaan, the Latin word is rather from Proto-Italic *ōs- "mouth," from PIE *os- "mouth" (see oral). He writes:

The chronology of the attestations shows that 'to plead, speak openly' is the original meaning of orare .... The alternative etymology ... seems very unlikely to me: a connection with Skt. a-aryanti 'they acknowledge' and Ru. orat' 'to shout', since nothing suggests a meaning 'to shout' for the Latin verb, nor does it seem onomatopoeic.

The general meaning "public speaker," is attested from early 15c. Fem. forms were oratrice (early 15c., from Anglo-French); oratrix (mid-15c., from Latin); oratress (1580s).

"formal public speaking; the art of eloquence," 1580s, from Latin (ars) oratoria "oratorical (art)," fem. of oratorius "of speaking or pleading, pertaining to an orator," from ōrare "to speak, pray, plead" (see orator).

Oratory is the art or the act of speaking, or the speech. Rhetoric is the theory of the art of composing discourse in either the spoken or the written form. Elocution is the manner of speaking or the theory of the art of speaking ...: the word is equally applicable to the presentation of one's own or of another's thoughts. [Century Dictionary]

compound adjectival word-forming element, usually interchangeable with -ic but sometimes with specialized sense (such as historic/historical, politic/political), Middle English, from Late Latin -icalis, from Latin -icus + -alis (see -al (1)). Probably it was needed because the forms in -ic often took on a noun sense (for example physic). Forms in -ical tend to be attested earlier in English than their twins in -ic.