Ill or sick?

"Ill" and "sick" can be used interchangeably. It's just a matter of prefence, although "ill" can be a bit more formal than "sick".

P.S. Here's an interesting note: In some parts of the southeastern U.S., "ill" can be used to say that someone is disgruntled or in a bad mood. (Ex. She's been ill all day. = She's been in a bad mood all day.)

I agree with Anon. An ill-tempered person is one who is frequently disgruntled.

Does it depend on the object? We can say 'sick man' but can we say 'ill man'?

I've heard "This is an ill man!" for emphasis, but it's certainly less common than "This is a sick man!"

I wouldn't recommend calling the noun which an adjective modifies "it's object," but I knew what you meant.

Thank you!