As Simon said, this is UK slang! It means to get EXTREMELY drunk or high – I've heard it more in reference to drugs than alcohol, but can be both, and definitely has a slightly negative connotation. Also, I've never heard 'get', it is more common to use this expression with 'be'. Ex. I saw him at the bar last night and he was off his face. You can't drive right now, you're off your face! I just had 5 shots of tequila, I'm gonna be off my face.

This is slang, specific to the UK I believe. Certainly quite a common turn of phrase in the part of England that İ come from (the south east). Here it is rewritten with synonyms that have the same meaning: - He just liked to get drunk/high/wasted/mashed every now and then. What’s wrong with that? Whether or not it is critical depends on the context in which it is used, as it could be positive, neutral, or negative.

I can confirm that it must be specific to the UK. I've never heard it in the US.