The House, beginning work yesterday on President Carter's omnibus energy bill, approved a program for local utility companies and the federal government to help insulate homes.

The debate then moved on to the multibillion-dollar controversey over whether to continue or remove price controls on new natural gas. The vote is expected today, and supporters of the President's plan to continue controls but at a higher level expect to win.

The home insulation program, approved 217 to 205, would require local utility companies to advise customers on their insulation needs. Government grants up to $800 would help low-income families insulate, and medium-income families could obtain low-interest loans.

By 1980, utilities would have to inform all customers of the benefits of insulation and offer to inspect their residences to determine their needs. Utilities loans and install insulation at there was an inadequate number of local suppliers. But federal officials could keep utilities out of the lending or installing business if it were considered anti-competitive. Utilities who were in the business of installing insulations as of April 20, when President Carter delivered his energy message, could continue.

The bill requires state governors to compile lists of lending institutions and insulation suppliers in each area for the benefit of residents. The close vote appeared due to the argument made by Republicans that governors might be tempted to list only their political supporters.

In other actions, all subject to reconsideration before passage of the bill later in the week, the House:

Voted 212 to 210 to order a study by the Department of Transportation of the potential energy savings from setting minimum energy standards for "off-highway vehicles; including non-commercial motorboats and aircraft. Gasoline mileage requirements for automobiles take effect with 1979 models this fall. Opponents called this another case of government control of private possessions.

Voted 252 to 166 to order another DOT study of the energy potential offered by bicycles and how to eliminate obstacles to their use by commuters.

Authorized 317 to 105 a $65 million outlay to help local governments survey insulation needs in municipal buildings.

The bill also authorizes $900 million in grants over three years to help insulate schools and hospitals. Adopted 265 to 161 was an amendment applying to this construction work the Davis-Bacon Act requirements that workers be paid the prevailing local wage.

Also approved - as the House passed by the section without amendment - was a requirement that energy standards be set for major home appliances.