by all odds vs emphatically

by all odds and emphatically both are adverbs.

Word	Noun	Adjective	Verb	Adverb
by all odds	No	No	No	Yes
emphatically	No	No	No	Yes

As adverbs, by all odds and emphatically are synonyms defined as:

Other synonyms of by all odds include decidedly, definitely, in spades, unquestionably.

by all odds (adverb)	emphatically (adverb)
without question and beyond doubt	without question and beyond doubt