A combination of the words "gross" and "nasty", it is an adjective that goes above and beyond both terms. Can be applied to the hygene of an individual, food products, or any other situation where such a description is necessary.
Very similar to how "fugly" describes something exceedingly unattractive, using a combination of two words.
Jake: When I came in just now, I smelled the nastiest stench as I walked into our apartment. It was like a combination of Febreeze, ramen noodles, some other food and dust.
Jared: Let me smell it to see if I can find out what it is.
*sniff*
Jared: Oh man, that is just grossty.
A person who is grosty is both crusty and gross at the same time. A person who is grosty usually will have greasy hair, smell like body odour and have a geeky or weird personality. They usually will not bathe reguarly.