Washington-based USAir said yesterday it has placed a $330 million order for 15 new jetliners with the Boeing Commercial Airplane Co. as part of a program to expand and modernize its fleet.

USAir exercised an option to purchase 10 new 737-300s and added five 737-200s to the order. The 737-200 is a "shelf-item" airplane, available for delivery; the 737-300 is Boeing's newest model, and the first copy--for delivery to USAir--is expected off the production line next January.

The order from USAir brings to 40 the number of firm commitments from five airlines to purchase 737-300s, a Boeing spokesman said yesterday. More than 1,000 earlier model 737s have been sold worldwide to 113 airlines.

The USAir purchase is a boost for Boeing in its heated competition with McDonnell Douglas to sell short-haul, fuel-efficient airplanes in a depressed market. Douglas is busy trying to sell the DC9-Super 80, which has attracted much recent attention locally because it is quiet enough to land legally at Washington National Airport after 10 p.m.

The Super 80--which McDonnell Douglas is in the process of renaming the MD80--has been available since 1980. So far, 124 have been delivered worldwide and another 72 are on order.

USAir--a major tenant at National--chose the 737-300 over the MD80 in March 1981 and placed part of the order that permitted Boeing to launch the 737-300. Preliminary noise estimates for the 737-300 indicate it will just fail to meet the late-night limit at National.

The MD80 is still in hot competition for two other big orders expected shortly. Both Boeing and Douglas have been busy wooing British Airways, which is expected to buy about 25 new airplanes, and Japan Air Lines (JAL), expected to buy about 10.

USAir's 737-300s will carry 138 passengers; the 737-200s will carry 120. USAir's fleet consists entirely of short- and medium-haul aircraft, a fact that gave the airline a major advantage in the restructuring of the U.S. airline industry following deregulation. But some of those planes--including two early Boeing 727-100s and 26 British Aircraft Corporation 111s, are aging.