With the 1986 fiscal year already under way, Congress began moving in earnest yesterday to approve spending bills for this year that have been bottled up for weeks while the government has operated under stopgap funding authority.

Both chambers gave final approval to and sent President Reagan a $15.3 billion spending bill for energy and water programs this year. The energy and water measure is the only appropriations bill so far to clear both chambers. Congress is supposed to enact 13 annual appropriations bills to fund operations of the federal government this year.

The House has passed 11 of the spending bills, including an $8.4 billion military construction measure approved yesterday, 373 to 36.

The bill is $1.9 billion less than Reagan requested. Among the reductions approved by the House were funds for expansion of some overseas bases.

The bill provided no funds to improve temporary airfields in Honduras. The House Appropriations Committee, in the report accompanying the bill, expressed strong concern about the "virtually continuous joint military exercises" the United States has conducted in Honduras, which borders Nicaragua, since 1983.

The Senate has approved four appropriations bills. Yesterday it began working on a fifth, providing $53.4 billion to fund the Housing and Urban Development Department and more than a dozen independent agencies, by voting to restore more than $600 million in cuts that were made to keep the measure within congressional budget targets.

The additions included $570 million in the government's general revenue-sharing program and $100 million for veterans' medical care.

An exasperated Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) linked the vote to increase the HUD bill with the Senate's passage last week of the mandatory deficit-reduction legislation sponsored by Sens. Phil Gramm (R-Tex.) and Warren B. Rudman (R-N.H.).

"For those who don't like Gramm-Rudman," Domenici said, "this is an example of exactly why we need it."

Domenici later succeeded in bringing the bill back within the budget targets. By voice vote, the Senate agreed to restore only half of the $570 million cut from revenue sharing and to impose a 1.1 percent cut in other programs funded by the legislation.

Last July, the Senate Appropriations Committee approved a $54.8 billion HUD spending measure. However, under pressure from the Budget Committee, this and several other bills were returned for additional cuts to bring them into line with the budget targets adopted by the Senate in July.

The Appropriations Committee responded by slashing $1.4 billion from the HUD bill, which included a 12 percent cut in the $4.6 billion general revenue-sharing program, slated for elimination next year.