Lit. “to have the oil in the head” is a bit old-fashioned but still mostly obvious way to say that a person is sensible or wise. On the other hand, people lacking these qualities are referred to with the contradiction: “nie ma oleju w głowie”.
Lit. “to spread around the bones” which is used to say that something expected to be really big resulted in almost no consequences, especially negative ones.
Lit. “to have a (strong) back”. In Polish, this expression has at least two metaphorical meanings. In most cases, this means: to have a strong political backing/support in your organisation, powerful friends that will help you in need.
Lit. “to eat (one’s) teeth on something” is an expression pointing that a person is very experienced in a given matter. You use it to elevate trust in a specialist, to stress that a specific task is a routine for her/him.
Lit. “next to the bone” is a human body description. It means: definitely not thin – might mean something like: bulky, big-boned up to chubby or fat, depending on who is talking and their intention.
