The phrase is casual and more common in spoken English rather than in formal writing. When you're chatting with friends, you can say you packed 'any old how'.
Pro Tip 2/3
Negative Connotation
Using this phrase implies something is done without much thought or effort. The manager didn't like that the report was put together any old how.
Pro Tip 3/3
Emphasis on Speed
The phrase can suggest the task was completed quickly, but without attention to detail. She set up the meeting room any old how.