You are a
At first, you will not object / That I am the case, matter and subject
"Case", "matter", and "subject" are all synonyms for TOPIC.
Change my third and I become / Noxious, venomous, even lethal to some
Change the 3rd letter to X, the word is now TOXIC. As in poisonous.
Change my third again then the bars and inns of the city / Are the place where you'll find me, very likely.
Change the 3rd letter to N, the word is now TONIC. As in gin & tonic water.
As for the title itself
Change the 3rd letter to E. The TOEIC is an English language test.