Eastern Airlines and three unions representing most of its workers negotiated past a midnight deadline last night as they sought agreement on concessions that would prevent the carrier from defaulting on its loans.

Talks with the airline's 4,000 pilots appeared to be the most troublesome. While the International Association of Machinists and the Transport Workers Union had signed agreements saying they would complete negotiations tonight, the pilots did not.

Although each of the unions has said it is willing to discuss concessions, there was no indication how far the three would go to help the airline. Without labor agreements by midnight last night, Miami-based Eastern would be considered in technical default on its $2.5 billion in loans. However, the banks probably would extend the deadline, sources said.

During 1984, Eastern's 37,000 employes agreed to pay cuts of between 18 to 22 percent in return for stock and four seats on the board. The 1984 concessions saved Eastern $370 million. The airline said it needs another cost-cutting plan to demonstrate to lenders that it could earn its first year-end profit in six years in 1985. Eastern lost $37.9 million in 1984, though its fourth period was its first profitable quarter in several years.