If you say something slangily, you are using words that are not formal or proper.
Slangily can make people think of being cool or casual, but also not very serious or important.
Examples:
He talks slangily with his friends.
She wrote the note slangily.
They spoke slangily about the movie.
I asked for directions, and he told me slangily.
The teacher talked slangily, and the kids thought it was funny.
She always talks slangily, and it makes her friends laugh.