The New Oxford American Dictionary 3rd Edition describes illegal as "contrary to or forbidden by law, especially criminal law", and describes unlawful as "not conforming to, permitted by, or recognized by law or rules." In American English, then, illegal is used in phrases like illegal alien, where it means a person present in a country without official authorization, and which is never replaced by unlawful.
Looking at the Oxford English Dictionary, I found a note about the usage of illegal and unlawful.
Illegal and unlawful have slightly different meanings, although they are often used interchangeably. Something that is illegal is against the law, whereas an unlawful act merely contravenes the rules that apply in a particular context. Thus handball in soccer is unlawful, but it is not illegal. A third word with a similar meaning is illicit: this tends to encompass things that are forbidden or disapproved of by custom or society, as in an illicit love affair.