之 = third person pronoun (it/him/her)
以 = with or indicating an indirect object
Verb 之以 Noun = VERB him with NOUN
In context, 淫之以色，啗之以利，养之以味，娱之以乐 means (a very rough translation) "(sexually) seduce him with sexy (women), lure him with benefit, accustom him with delicious food and amuse him with (obscene) music". It is included in a strategy saying that if you want to destroy your enemy nation, you need to first deceive (as in making him unable to make right decisions) the king then attack the military for the betterment of people. The sentence is detailing (figuratively) how you deceive the leader of enemy nation.