Mobil Corp., the nation's second-largest oil company, yesterday reported that its first-quarter profits dropped 16 percent because of financing expenses incurred in its $5.7 billion acquisition of Superior Oil Co.

Shell Oil Co., ranked seventh, said a 9.2 percent decline in its earnings for the January-March period reflected lower selling prices for crude oil, petroleum products, natural gas liquids and chemicals.

Sun Co., the 10th-largest oil company, blamed a 12 percent decrease on overseas exploration costs and price competition in Eastern coal markets.

Mesa Petroleum Co.. a smaller oil firm headed by corporate hunter T. Boone Pickens Jr., logged a 314.8 percent jump in its first-quarter earnings largely on the sale of securities and assets.

Analysts had predicted most major oil companies would show lower earnings for the January-March period because of surplus refining capacity and a steady erosion in petroleum-product prices early in the quarter.

New York-based Mobil earned $320 million (78 cents per share), down from $380 million (93 cents) in the opening 1984 quarter. Revenues were up 2.6 percent to $15.4 billion from $15 billion.

Mobil said financing expenses increased by $91 million to $179 million in the latest quarter primarily due to interest expense related to its purchase of Superior Oil.

Mobil Chairman Rawleigh Warner said stepped-up production of both crude oil and natural gas as well as increased product sales generated higher worldwide petroleum earnings.

Mobil's Montgomery Ward retailing subsidiary had a $2 million loss in the quarter, and its chemical operations had a $7 million loss.

Shell, headquartered in Houston, earned $296 million (96 cents), down from $326 million ($1.05) in the first quarter last year.

Sun, based in Radnor, Pa., said its first-quarter earnings dropped to $127 million ($1.12) from $143 million ($1.23) a year earlier. Sales were down 12.8 percent to $3.67 billion from $4.21 billion.

Sun Chairman Theodore Burtis said the smaller decline in per-share earnings was because of the reduction in the number of shares outstanding, which was part of the company's stock repurchase program.

In Amarillo, Tex., Mesa Petroleum announced its first-quarter earnings rose to $51.1 million (73 cents) from $12.3 million (10 cents) a year earlier. In the latest quarter, Mesa had a $75.2 million pre-tax gain on the sale of securities and assets, part of which was offset by $50.7 million in interest costs primarily associated with financing its investment in Unocal Corp.