These words are dialectal, appearing only in regional speech and never in formal writing. They mean "at any rate," "in any event," or "at least": "Leastways, that's what I thought he said." "You could leastwise try harder." Both words are highly informal conversation fillers and should not be used in writing or speech unless employed for the purpose of characterizing an uneducated person.
Dictionary of problem words and expressions. Harry Shaw. 1975.