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1.
To be VERY much under the influence of a substance. Most commonly used as either an excuse or a conversation starter.

A variation of sozzled
"I only kissed him because I was off my tits" OR "God, I was so off my tits last night, I don't know how I got home"
by The Traveller July 28, 2005
 
2.
Basically extremely intoxicated, blurred vision and beer goggles are all part of the deal.
Ann: God last night was good!
John: ah yeah, was good can't remember much, was with some fat bird I think but it's okay, cus I was off my tits!
by MirreyBirrey May 17, 2010