Norfolk Southern Corp. yesterday sought to remove the remaining Justice Department objections to its proposed acquisition of Consolidated Rail Corp. by offering to share access to a major high-speed Midwest freight line with a competing railroad.

The plan was enthusiastically endorsed yesterday by the competitor, Guilford Transportation Industries, a New England and New York State freight line that would gain an advantageous freight route to St. Louis under the new proposal. The Justice Department's antitrust division won't approve the Conrail sale until it is satisfied that Guilford won't be hurt competitively.

There was no reaction yesterday from the antitrust division, which now controls the switch on the issue within the administration. Transportation Secretary Elizabeth Hanford Dole has picked Norfolk Southern to take over the government's railroad, but has deferred to Justice on the antitrust issue.

And even if the Reagan administration's reservations about the sale of Conrail to Norfolk Southern are resolved by the new proposal, there still is strong opposition in parts of Congress. The impact of the deal on three midwestern grain-shipping lines isn't an antitrust issue, but it is a political question that has helped hold up congressional approval. House sources said the new Norfolk Southern proposal will be closely examined, and it wasn't clear whether yesterday's move will get Congress moving on the issue.

Norfolk Southern clearly hopes so. "Today's action should remove any excuse for further delay," said Robert B. Claytor, the railroad's chairman.

Last June, Norfolk Southern had proposed to sell Guilford several rail lines connecting Chicago, northern Ohio and St. Louis, in hopes of meeting the antitrust division's divestiture requirements. That proposal, however, failed to satisfy the government's lawyers and Norfolk Southern's congressional opponents.

Now, instead of selling Guilford rail lines between northern Ohio and St. Louis, Norfolk Southern proposes to rent Guilford the right to use the Conrail mainline track from Toledo to Ridgeway, Ohio, and from Crestline, Ohio, to St. Louis. From Guilford's standpoint, the change is a big plus, said Guilford Vice President F. Colin Pease. He promised that shippers would benefit from vigorous competition between the two railroads over the shared rail line.

The original plan called for Guilford to purchase a second-rate freight line to St. Louis that has a 40 mile-per-hour speed limit and requires $40 million in renovation.

Under yesterday's plan, Guilford would get access to a 70-mph Conrail track from Ohio to St. Louis -- the same line Norfolk Southern will use if the Conrail deal goes through. Norfolk Southern yesterday guaranteed Guilford equal access to that line at a bargain price that won't even cover track maintenance expenses, a Norfolk Southern official said. Guilford also would benefit from a lower price for the remaining track it would buy -- reduced from $50 million to $35 million.

"In effect, they [Guilford] get virtually a free ride to compete with Norfolk Southern," said J. Paul Molloy, an attorney for Norfolk Southern.