Federal and postal unions that normally spend time and money battling each other for turf, publicity and members, are working together to help striking air traffic controllers.

National leaders of U.S. unions representing more than a million civil servants are taking a variety of actions -- from the symbolic to cash on the line -- to help the embattled Professional Air Traffic Controllers Organization stay alive so the Reagan administration won't be tempted to eat them next.

Examples:

The National Association of Letter Carriers and the American Postal Workers Union each donated $5,000 to assist fired PATCO members. They have asked members to send more money, earmarked for the controllers, to headquarters. Both unions are sweating out a membership mail ballot that will determine whether they keep working or set up their own picket lines outside post offices.

The American Federation of Government Employees, like PATCO an AFL-CIO affiliate, and AFGE's arch-rival, the independent National Treasury Employees Union, are supplying public relations and legal talent to help battle government efforts to strip PATCO of its right to represent controllers.

AFGE chief Kenneth Blaylock, who is a member of the AFL-CIO executive board and president of its Public Employees Department, is trying to get organized labor to maintain a pro-PATCO united front and persuade other AFL-CIO union leaders -- some of whose members are being laid off because of the PATCO strike -- not to give aid and comfort to government hard-liners who believe they have congressional and public opinion on their side.

The National Federation of Federal Employees, a comparatively conservative independent union with a high percentage of middle- and upper-grade members, has blasted the White House and asked that bargaining be resumed.

Lawyers from at least two unions, NTEU and AFGE, are helping the PATCO law firm (Leighton, Conklin, Lemov, Jacobs & Buckley) with legal research. For the often-warring unions, this is like the United States and the Soviet Union teaming up to protect a smaller nation from outside aggression.

Friendly feds are monitoring 66 separate actions -- before courts from Vermont to Mississippi -- against PATCO or individual members who allegedly violated their no-strike oath.

U.S. worker groups in Chicago are supplying food to PATCO members. In Madison, Wis., they have set up a "rumor hotline" to advise public and press of the "true" situation and stress that air safety, not money, is the primary strike issue.

Union locals in big cities have joined PATCO pickets and have spelled controllers on picket lines and acted as babysitters for people on the lines.

Although it is a long shot, the unions have promised to lobby for H.R. 4375, a bill introduced by Rep. John Conyers (D-Mich.) just before Congress left on vacation. His bill would give federal workers the right to strike and -- if passed before Dec. 31 -- legalize any government strikes this year.

Federal union leaders are using radio talk shows, TV interviews and the like to warn their own people that they consider the PATCO affair the beginning of a White House scheme to bust all government unions.

This week's issue of U.S. News and World Report, for example, features a debate between postal union leader Moe Biller and Transportation Secretary Drew Lewis in which Biller says the controllers should be granted amnesty because Uncle Sam forced the strike. Lewis says controllers broke the law. (Ironically, postal unions have been unable to get amnesty for postal aides fired several years ago for striking.) "If PATCO loses," one union official said, "we know we are next."