Vice President George Bush arrived today in this most powerful of black Africa's nations, on the third stop in a scheduled seven-nation tour. The Reagan administration's relations with Nigeria have been strained by U.S. dealings with white-ruled South Africa.

The White House has announced that Bush will head the U.S. delegation to the funeral of Soviet president Leonid Brezhnev. Although the departure time was not yet clear, a spokesman said Bush will return to Africa after the funeral and visit all countries previously scheduled. He was scheduled to remain here until Sunday.

Bush, with a nod to the concerns of his Nigerian hosts, announced on arrival that "together, we will discuss the surest means to advance freedom in Namibia." A major U.S. initiative, now apparently stalled, is aimed at achieving independence of that territory now ruled by South Africa in defiance of United Nations demands.

As black Africa's largest democracy, Bush continued, "Nigeria holds a position of critical importance" on such continent-wide issues.

In separate interviews this week, a senior Nigerian foreign policy official and a high-level U.S. diplomat both said there is a growing "unease" in the once warm relations between the two trading partners.

"There hasn't been any movement whatsoever" on achieving Namibia's independence since the Reagan administration took office, said the senior Nigerian official.

The American said an objective of Bush's visit is to address this issue. The Nigerian official, however, said he did not expect anything "substantive" from Bush's scheduled meetings with President Shehu Shagari, Vice President Alex Ekueme and Senate President Joseph Wayas.

Beginning in the mid-1970s, when oil prices began to rise dramatically, the United States has bought about half of Nigeria's oil exports. By 1980, Washington's trade deficit with Lagos had climbed to $9 billion due to crude oil purchases. The deficit is expected to be $6.5 billion this year.

Bush visited Cape Verde and Senegal before arriving here. His itinerary includes Zambia, Zimbabwe, Kenya and Zaire.