"He is a liar as hell" sounds rather unnatural. "As hell" is an adverbial expression. That being said, it is more often than not used to provide additional context/description for verbs and adjectives. Since "a liar" here is a noun, "a liar as hell" doesn't sound all too natural, though it can be used as colloquially. Just a pointer.
As for expressing the idea of "lying constantly", there are many ways, from formal to informal, of conveying and getting the same point across.
Though it IS an actual mental illness, a "pathological liar" is and can be used as a rather commonly used metaphoric expression to refer to someone who lies A LOT. For example, "he is a borderline pathological liar, running his mouth like a faucet all the time". The later part of the sentence implies that he tells a lot of things which aren't necessarily true (basically, a lot of stuff coming out of his mouth is garbage). Speaking of which, you could be more pejorative about it and just say "stuff that comes out of his mouth is mostly garbage". Another alternative would be "he breathes lies 24/7"; here you are basically replacing the action of "having a meal" with "breathing", which insinuates the person in question lies "constantly". Some other expressions along the same lines are "habitual liar", "compulsive liar". Hope this helps.
