The story of the Transportation Department's attempt to sell Conrail, according to sources on several sides of the issue, will get curiouser and curiouser now that it has found its way to Capitol Hill.

What Transportation Secretary Elizabeth Hanford Dole hopes for -- a nice, quick decision from Congress -- would be unlikely under the best of circumstances but is especially improbable when budgets are tight and lawmakers are looking for measures to which they can attach strings. Conrail provides a whole trainload.

For example, the president's new budget shows a $1.2 billion gain from the sale of Conrail and a $684 million savings by eliminating all subsidies for Amtrak, the national passenger railroad. Amtrak says such action means the end of Amtrak, not just its subsidies.

Anyone who can't propose a legislative deal from that set of circumstances flunks Politics 101.

The states most affected by Conrail and Amtrak, not to mention the proposed elimination of most urban transit subsidies, are the same northeastern states. The key congressional subcommittee for both railroads is the House Energy and Commerce subcommittee on commerce, transportation and tourism, chaired by Rep. James J. Florio (D-N.J.).

Florio has complained for more than a year that Dole was shutting him out of the Conrail decision-making process, and he has scheduled hearings on the issue, beginning Feb. 27, to study only the process by which Dole chose Norfolk Southern as the Conrail buyer. He will get to substance later.

On the same day, the Senate Commerce Committee has chosen to kick off its Conrail hearings. Both the Senate and the House will want Dole as the leadoff witness and the Senate got its bid in first, which will give Florio an opportunity to complain that, once again, Dole is not responsive to his subcommittee's needs for information. THAT'S NOT ALL, FOLKS . . .

The Congressional Rail Game this year will also include an attempt by disgruntled shippers and others to reregulate railroad freight rates, especially for coal, grain and other bulk commodities that move best by rail and thus are "captive" traffic.

A group called Consumers United for Rail Equity (CURE) will launch its legislative campaign next Wednesday to eliminate some of the rate-setting freedoms granted in the deregulation law, the Staggers Rail Act of 1980.

However, the Reagan administration has already said it strongly opposes any reregulation efforts and another group, the Committee Against Revising Staggers (CARS), is hoping to derail CURE. CARS consists primarily of shippers who have a choice between rail and truck and have enjoyed the lower shipping costs created by competition. CLEANING UP CONRAIL . . .

Another tangled chapter in the Conrail story came to an end this week. United States Railway Association Chairman Stephen Berger announced the resolution of a nine-year legal battle to settle claims against the U.S. government brought by Penn Central and other bankrupt railroads whose properties were transferred to Conrail.

The USRA was created by Congress to oversee reconstruction of northeastern rail service. The settlement of the last lawsuit came when the Supreme Court affirmed a special court judgment granting $42.5 million to the successors of the Central of New Jersey, one of the defunct railroads now in the Conrail system.

The other railroads included some of the best names in railroad lore, the Erie Lackawanna, the Reading, the Lehigh Valley, the Lehigh and Hudson River and the Ann Arbor. Total settlements previously reached were $2.8 billion, a significant cut from the $16 billion in claims originally filed. REORGANIZATION IS PROGRESS . . .

The Urban Mass Transportation Administration would suffer a $2.7 billion cut under the president's budget, which would wipe out all but $1.1 billion in federal transit aid now earmarked from highway taxes.

But there is always the private sector, and UMTA Chief Ralph L. Stanley took a bold move to tap it Wednesday when he created a new Office of Private Sector Initiatives, temporarily under the direction of Doug Birnie. The press release announcing the program said, "Anyone interested in exploring the use of the private sector in improving public transportation is encouraged to contact" the office at (202) 426-6385.

Don't all call at once.