'any old how' I think is a very old southern American thing to say, but generally never formally written (save maybe if you're writing how you're talking in a blog). We also don't say "old", rather "ol'" so "any ol' how" would be more common to hear, but still isn't a common thing to hear much anymore, and I haven't heard anyone using it since I left the south. As stated 'any which way' is more common and similar and also changed to "any which-a-way" when spoken.

I don't think this phrase is commonly used, but it seems similar in meaning to "any which way". More examples: http://oxforddictionaries.com/us/definition/english/any%2Bold%2Bhow___1 any (old) how SPOKEN in a careless and messy way Don't just stuff your things into the drawer any old how.http://www.macmillandictionary.com/us/dictionary/american/any

I agree with Rochella. You would not hear this in most parts of the world (probably only by someone in the southern US that is 50+ years old). The way most people in the US would say this conversationally is, simply, "anyhow" or "anyway".

I must correct myself. I meant to say I would not use this in a sentence.

Sorry this does not make sense to me. I wouldn't use it in sentence.