Ore ga = I (ga is a particle that marks the subject, so "I" is the subject)
Boost is, well, boost. Unsure if the word is meant to be a verb or a noun with the copula being omitted. (Context is necessary here!)
"Ore ga BOOST!" could be:
1. "I boost!" or "I will boost!"
2. "I am boost!"
The second possibility is awkward, so I think it's the first.
I'm almost sure that, going by the meaning of the word on Jisho.org, "Furuitatsu GHOST!" is "Ghost that cheers up." The verb is coming before a noun. The main verb of a sentence in Japanese comes at its very end, so if a verb comes before a noun in the middle of a sentence, that verb is an action done or being done by that noun.
That phrase is making my head spin, though, with the gratuitous English words inserted into it. Do you happen to be watching anime or something? Usually in such shows, the kind of language used is somewhat more stylized or exaggerated in a way that doesn't quite match how Japanese is spoken normally.
Learning Japanese through anime is a foolish thing to do when learning the language for the first time. It's good to improve vocabulary, though.
I'm tagging
PushDustIn
anyway to see if my interpretation is anything reasonable. After all, my Japanese skills aren't anything remotely good, but I hope I could help clarifying something.