*Grotesque* means "freakish":

The very notion of a musical production of *Anne Frank* is grotesque.

*Gross* is a synonym of "blatant".

Brady's composition for his freshman English class was filled with the kind of gross errors that one might expect from a six year-old, but that are simply unacceptable at the college level.

I hope this helps.

grotesque. Roget s II: The New Thesaurus, Third Edition. 1995.
...Conceived or done with no reference to reality or common sense: antic, bizarre, fantastic, fantastical, far-fetched. See TRUE, USUAL. 2. Resembling a freak: freakish,...

Brutishly coarse, as in behavior; crude: “It is futile to expect a hungry and squalid population to be anything but violent and gross” (Thomas H. Huxley).

there are some cases where they could describe the same thing:
a freakish disgusting thing

I think you would use them differently. "Grotesque" sounds a little more specific, and also frightening, than "gross." So when I hear "grotesque" I think monsters, disfigurements, candles-in-the-dark-lighting-up-spooky-faces kind of thing. "Gross" is slang and I wouldn't use it in writing, unless it's a dialogue. It generally means "disgusting" and is used to refer to anything from snot to disgusting-looking food, to a disgusting topic of conversation. It's a bit young, too, I think--we usually think of teenagers talking about, say, food being "gross." Hope that helps!