Chrysler Corp. reported yesterday the largest quarterly loss in business history.

During the July-September period, the automobile manufacturer said, losses added up to $460.6 million compared with a loss of $158.5 million in the same period a year earlier, as sales fell 14 percent to $2.5 billion.

Moreover, in a report to stockholders, Chrysler executives expressed gloom about the fourth-quarter outlook for the entire automobile industry and said the company's available working capital has been reduced substantially.

Although Chairman Lee Iacocca said he expects "quick and positive action" on the company's request for federal loan guarantee assistance to remain in business, two key Senators yesterday raised new questions about Chrysler's strategy for survival over the next five years.

In a letter to Treasury Secretary G. William Miller, Senate Banking Committee Chairman William Proxmire (D-Wis.) and ranking GOP panel member Jake Garn of Utah said Chrysler to date has not provided adequate information to back up projections of an increased share of the market. Nor, they said, is there enough information about the impact on competitors if aid is given to one company or what would happen if optimistic assessments about the auto business and Chrysler's condition do not materialize.

Specifically, Proxmire and Garn said Chrysler's strategy makes it clear that the company intends not only to remain in all lines of the auto business but also to expand its market coverage by means of a $13.6 billion capital investment program to be supported by federal guarantees.

". . . It does not necessarily follow that Chrysler will sell more cars . . . (nor that profits earned through this expanded market coverage will be sufficient to offset the additional costs of development and marketing," the senators said.

The tough new line of questioning by Proxmire and Garn came as Miller was completing work on the Carter administration's proposal to provide loan guarantee assistance to Chrysler. The senators' letter indicated that it will be difficult to get any aid package for the auto firm through the Senate this year although House passage is considered likely.

Iacocca told Chrysler stockholders yesterday that the company's third quarter loss "is further indication that this company is on the cutting edge of developments which have serious possible consequences for the entire automobile industry . . . government regulations, fears over gasoline availability, and the spreading recession have caused even our largest competitors to report pre-tax losses for the third quarter."

He was referring to reports last week by General Motors and Ford Motor Co., both of which listed a sharp decline in profitability. A $121 million tax credit allowed GM to post slim profits of $22 million, down 96 percent from a year ago. Ford benefited from a British tax law change of $186 million, which produced overall net income of $103 million -- down from $301 million a year ago.

In its earnings statement, Chrysler revealed:

Worldwide vehicle sales in the third quarter fell to 353,000 units from 474,000 a year ago while nine-month sales declined to 1.34 million from 1.64 million.

Nine-month losses mushroomed to $721.5 million from $247.8 million in the 1978 period as total sales fell to $8.9 billion from $9.6 billion.

In the U.S., auto sales for the first nine months were 879,900 units compared with 962,900 a year earlier, reducing Chrysler's share of the domestic market to 10.7 percent form 11.2 percent. Truck sales plummeted to 277,000 units from 375,000 and Chrysler's truck market share fell to 10.2 percent from 12.1 percent.

Available working capital was only $356 million on Sept. 30 compared with $959 million a year ago, at a time when Chrysler is projecting spending $160 million a month for plants, new tools and products.

During the recent quarter, Chrysler conducted a successful rebate program to reduce its inventory of unsold vehicles to 27,000 from more than 80,000 -- but the cost to the company was more than $100 million.

In addition, Chrysler delayed the introduction of 1980 models and curtailed production schedules at a cost of about $195 million.

"Many of these adverse factors will continue through the fourth quarter," said a company statement. "Because industry retail sales are expected to remain at depressed levels, the company is reducing production schedules for the balance of the year . . .Chrysler will report a loss for the fourth quarter."