The House gave overwhelming approval to a bill authorizing an $800-million increase for military construction for the current fiscal year. The measure, approved 354 to 38, will allow the Defense Department to spend $9.2 billion for hundreds of construction projects this year, compared to $8.4 billion for fiscal 1985. The Reagan Administration had asked for $10.3 billion. One major project in the bill is $86.2 million for construction of a Navy base on Staten Island, N.Y., to house the renovated battleship Iowa. The Iowa is one of four World War II battleships to be brought out of mothballs and overhauled.