Used in this way, "hoot" means the least bit of concern, I do not care. "I don't give a hoot." means I don't care, even a little bit. So, I don't give a hoot and a half just means "I really, really don't care." You can say any number of hoots (two hoots, three hoots, etc.). By the way, the sound that owls make is also called a hoot.

toby1218, "Hoot" has another meaining besides the one already mentioned. a hoot.....an amusing person or thing. a hoot and a half....a very amusing person or thing. ----from The Big Bang Theory" season three episode one--- Leonard Hofstadter: Oh,thank God we're home! Howard Wolowitz: I can't believe we spent three months in that frozen hellhole. Rajesh Koothrappali: It was like a snowy hell from which there was no escape. Sheldon Cooper: I don't know what arctic expedition you guys went to. I thought it was a hoot and a half. Apparently Sheldon though that the expedition was a lot of fun.