Worf obviously knows Klingon as he has been seen translating Klingon phrases for his Federation colleagues.
Gowron: We shall see. (in Klingon) CHEGH-chew jaj-VAM jaj-KAK!
Worf: He said, "Today is a good day to die."
But having been mostly raised by humans, he would be proficient in English as well (or Russian possibly... but an Earth language nonetheless).
So, what language does Worf regularly use throughout the shows? Does he speak Klingon and let the Universal Translators do their job or does he speak English, switching it up while in Klingon company?
Why this question is interesting:
Klingons tend to look down on Worf for "abandoning" his Klingon heritage in favor of Federation ideals. Despite his efforts to be as Klingon as possible, he's still an outcast among his people. If Klingon isn't his native language and he speaks it with an accent or speaks in English instead, it gives Klingons another reason to think of Worf as an outsider no matter how many times he proves his honor in other ways.
I'm aware of the inconsistencies in the way the universal translators decide to translate, especially when dealing with the Klingon language (which is what makes this question so hard for me to figure out on my own). What I'm looking for is something in the dialogue or some other sort of reference that indicates what language he's using. Perhaps a Klingon who pokes fun at Worf's accent/improper use of the Klingon language or looking down on him for spending most of his time speaking like a human. Something like that.