Prince George's County public employes union gave notice yesterday that its 1,500 members will walk off their county government jobs March 18 unless the union's long-standing contract dispute with the county is settled.

If the members of the American Federation of State, County and Municipal Employees go on strike, the county will be without the services of its jail guards, road maintenance crews, landfill operators and building inspectors as well as clerical and other workers vital to operating the county government. Police officers and fire fighters are not members of the union.

The union announced the strike date early yesterday when it delivered a 10-day notice to the office of County Executive Lawrence J. Hogan, who has repeatedly vetoed various agreements that his negotiators have reached with the union.

The 10-day notification is required by the county's labor code before the union can legally strike. Prince George's is the only jurisdiction in the Washington area where public employes have been given the right to strike.

Hogan released a statement calling the union's decision to strike irresponsible and illegal. "I have activated the county's emergency strike plan and we will offer protection to all employes who choose to work," his statement said.

Announcement of the March 18 deadline followed more than a year of negotiations between the county and the union. Since the union's last contract expired in July, its members have been working without the cost-of-living raises granted all other county employes.

Three weeks ago, it appeared that the contract dispute had been settled when negotiators for the union and the county signed a tentative agreement granting the employes raises of 4.7 percent this year and 5 percent next year. Hogan's negotiators considered it quite favorable to the county.

Hogan vetoed that agreement the same day. His reasons for doing so have become a matter of controversy and the subject of an unfair labor practice grievance filed by the union, whose members had already approved the agreement.

Hogan said he found several provisions in the contract unacceptable and declared that his negotiators had exceeded their authority in signing the agreement.

County officials close to Hogan said he refused to sign the agreement because he feared that recent political squabbles with the County Council and particularly its chairman, Parris Glendening, a possible Hogan opponent in the 1982 county executive's race, would make it look as though he capitulated. Hogan is a Republican; Glendening and all the other council members are Democrats.

Hogan reportedly told his aides and negotiators that he would rather have a strike than allow the council to get credit for an agreement or have it appear that the union had been able to pressure him. He said at the meeting that he would support the agreement only if the union issued a statement criticizing the council and, specifically, Glendening.

Hogan has denied that he vetoed the agreement for these reasons or that he would have approved it if such a statement has been issued.

At a three-day hearing this week before an outside hearing officer on the unfair labor practices charge, Hogan's own negotiator stated that political considerations had played an important role in Hogan's decision to reject the tentative agreement.

The negotiator said at the hearing that Hogan "was concerned about what had appeared in the newspaper and overall he felt there was a plan to politically challenge him. He thought (the union) and the County Council had agreed to team up on him, and in concert they were going to elect a council member as the new county executive."

The hearing officer said he does not expect to rule on the charge for at least several days. The union has requested that the mediator force Hogan to accept the tentative contract. Hogan's attorneys have argued that he had the right to veto the contract because his negotiators had exceeded their authority and Hogan's own instructions.

Since Hogan rejected the agreement, the county and the union have met several times to iron out their differences without success. Last week they met with federal mediators in what was billed as one last effort to resolve the three or so outstanding issues, including some holiday provisions and county payments for minor medical insurance.

At that session, Hogan's negotiators reported that the county executive was also objecting to 12 more provisions of the tentative agreement, an announcement that caused union representatives to accuse Hogan of stubbornly forcing them into a strike.

Hogan said in turn that of the 12 provisions, 10 were out of line with the county's personnel laws. The other two, he said, would benefit only union leadership, including one provision that would allow a county-paid, full-time shop steward.

Hogan has also recently claimed that a strike by county employes would be illegal because the labor code allows for a strike only if a complete impasse has been reached. Although a mediation board ruled in December that such an impasse had occurred, Hogan has requested they change that ruling because of recent discussions between the two sides.

Ernie Crofoot, the union's state executive director, said yesterday the union is organizing a fund to help support the families of striking workers. He also said other unions in the county have indicated they will help strikers either by contributing funds or time to the effort. Crofoot said the union will not ask other unions to walk off the job in support.