Relationship between PP and PH
No, it's not known whether $PH \subset PP$, and it's not known whether $PP \subset PH$.  Neither of those is implied by Toda'a theorem.

This blog article cites a paper by Beigel giving some weak evidence to suspect that $PH \not\subset PP$ (that $PH$ is not contained in $PP$).  Please be warned that this is very weak evidence and doesn't really prove anything.  The result says that there's a relativized world where $P^{NP}$ is not contained in $PP$.  It follows that there's a relativized world where $PH$ is not contained in $PP$.  This might suggest the conjecture that $PH \not\subset PP$.  Or, at least, it suggests that proving $PH \subset PP$ might require special proof techniques (non-relativizing proof techniques; and most, but not all, known proof techniques do relativize).