Recovering rapidly from the wounds of last spring's supermarket war, Giant Food Inc. reported yesterday it has returned to a level of profitability that is higher than it was a year ago.

Hechinger Co. also reported its profits jumped sharply in the third quarter, despite a general malaise in the retail business.

Riding a 19.9 percent increase in sales, Giant earned $6.77 million ($1.38 cents a share) in the three months ended Nov. 7.

The third-quarter profit contrasted with Giant's $2.41 million loss in the previous three months and was better than twice the $3.16 million (65 cents) that Giant earned in the same three months last year.

Giant's computerized checkouts rung up $398.4 million in the quarter compared with total sales of $332.2 million last fall.

The improvement in earnings is most evident when Giant's profits are measured as a percentage of total sales.

In the latest quarter, the food chain earned 1.7 percent on sales--$1.70 profit on every $100 worth of merchandise sold. In the fall of 1980, Giant's earnings amounted to less than one percent of sales, and during the past five years, annual earnings have ranged from 1.23 percent to 1.57 percent of sales.

Even with the sharp gain in the past three months, Giant profits are still well below par so far this year. For the 36 weeks ended Nov. 7, Giant earned $4.5 million (92 cents), equivalent to 0.4 percent of its sales of $1.13 billion. In the same period a year earlier, Giant earned just over $8 million ($1.64) or 1.38 percent of sales of $968 million.

Giant officials attributed the strong quarterly performance to the nearly 20 percent increase in sales, which appears to indicate Giant took business away from competitors during the spring and summer price war.

Also boosting the quarterly earnings were two accounting adjustments, the company noted. Because of its losses earlier this year, Giant is paying less income tax than last year; LIFO accounting charges also have been reduced, further aiding earnings.

Hechinger reported an even bigger sales gain than Giant, with revenues from its 31 stores increasing 26 percent to $54.4 million from $43.3 million in last year's fall quarter.

Profits of the Washington do-it-yourself chain jumped 29 percent to $2.2 million (30 cents) from $1.7 million (25 cents).

More than half the sales gain resulted from opening new stores, the company said, but sales of units that were open at this time a year ago were up 12 percent for the quarter and 14 percent for the first nine months of the fiscal year.

For the 39 weeks ended Oct. 31, Hechinger earnings increased 32 percent to $6.2 million (84 cents) from $4.7 million (71 cents) while sales climbed 27 percent to $164 million from $128.9 million.

Hechinger also announced yesterday it has started work on a new store in the Baltimore area at Security Mall and plans to build and open new units next summer at Columbia and near Philadelphia