DUSSELDORF, Germany, Feb. 5--West Germany embarked today on a vigorous drive designed to counter the Soviet bloc's economic overtures in Asia and Africa.

Five leading West German industrialists left today on a six-week good will mission to Far Eastern countries. Tomorrow, Alfred Krupp, head of the vast Ruhr concern, departs for a tour of India, Pakistan, Thailand, and Egypt.

Later this month, Professor Kurt Tank, former Luftwaffe designer, sets off with a staff of 20 assistants under a contract to build up India's aircraft industry. Economics Minister Ludwig Erhard will visit Britain Feb. 20-25 to discuss possible concerted counteraction against the Communist trade offensive.

Seeks Investigation

WASHINGTON, Feb. 5--Sen. Knowland (R-Calif.) called today for a speedy investigation of whether money had been offered Sen. Case (R-S.D.) to influence his vote on the natural gas bill.

The GOP leader said he would join with Senate Democratic Leader Lyndon Johnson of Texas in offering a resolution tomorrow to set up a special committee to develop all the facts about the $2,500 campaign contribution offer reported by Case.

May Cancel Tour

LONDON, Feb. 5--Russian attacks on British colonial policies are giving Britain second thoughts about its invitation to Soviet Bulganin and Communist party chief Khrushchev to visit London in April.

A government source said that unless Moscow's propaganda campaign is toned down the Soviet visit, heralded as a "good will tour," might be cancelled.