Hello,
"Overwhelmed" is no synonym with being drunk at all ,
It is usually used passive to mean as you mentioned to defeat someone , or to cause someone to feel a sudden strong emotion ,but could also be used in a positive sense " She was overwhelmed by all the flowers she received " .
Other ways to express " being drunk " :
There are lots of slang words to indicate that state such as :
" besotted , blind drunk , blotto , crocked , loaded , smashed , soaked ,tipsy , narcotized , half-seas-over, high , mellow , drunken ,boozy , orgiastic beery ,slopped , fuddled ......"