"Screwed" essentially means "cheated" here, much as it does today.
"Blewed" meant "lost or been robbed of". The word's origin is from the German "blauen" so it's actually related to "blue", not "blew", and meant that something had vanished (into the blue). (According to "A Dictionary of Slang, Jargon & Cant" By Charles Godfrey Leland, published in 1889.)
"Tattooed" refers here to a beating with very rapid blows, in the same sense as a military tattoo, which is a rapid pattern on a drum.
So, the phrase literally meant "cheated, robbed and beaten".