Letters from American hostages in Tehran continued to arrive in the United States yesterday, bearing messages of hope and despair, criticism of President Carter, appeals for help and thanks for the American public's support.

Some letters offered glimpses of life in the U.S. Embassy, seized by Iranian militants Nov. 4. "The students came to our room tonight, where five of us hostages are living and dumped a stack of (Christmas) cards and told us, if we wished, we could answer them, supposedly," Marine Sgt. Rodney V. Sickman of Krakow, Mo., wrote Dec. 23. "It was great."

By yesterday evening the State Department reported that 3 letters had been received in the last few days from 17 of the 50 American hostages in Tehran. The most dramatic letter appeared to be one published yesterday by the Washington Post from Robert C. Ode, 64, of Falls Church.

Ode, the oldest of the hostages, appealed for "prompt action to free us from this terrible situation" and described his confinement in stark terms, speaking of nearly sleepless nights, a lack of news, and days and nights spent with his hands bound.

Ode mailed similar letters to President Carter, Sen. John W. Warner (R-Va.) and Rep. Joseph L. Fisher (D-Va.). In his Dec. 26 letter to Fisher, Ode wrote, "We feel that we have been abandoned by our government and the American people and that our rights to protection as United States citizens have been and are being denied us."

White House spokesman Jody Powell said that Ode's letter to Carter "unfortunately. . . confirmed" the president's previous statements that the hostages are not being accorded adequate treatment.

The State Department, while expressing similar concerns about "the inhumane conditions" in which the hostages are held, expressed hope that the letters might be a more propitious sign. "We would hope that this indicates a new willingness on the part of the captors to allow the hostages to communicate with the outside world," said department spokesman Hodding Carter.

Sen. Warner praised Ode's letter as "a very courageous act" that would focus renewed public attention "on the fact that these hostages are being cruelly held." Warner also suggested that the Iranian militants' willingness to permit the hostages' letters to leave Iran may indicate fears by the militants that their cause has been "dwarfed" by last month's Soviet invasion of Afghanistan.

The letters -- all aparently written shortly before or after Christmas -- varied markedly. For example, Marine Sgt. Kevin J. Hermening, 20, an embassy guard whose family lives in suburban Milwaukee, wrote strikingly different letters to his mother and his father, who are divorced.

To his father, Hermening wrote in a political vein, saying, "I hope that if Carter hasn't returned the shah [to Iran] by next summer, that no one will vote for his reelection."

To his mother, the marine sergeant sent a personal message, lacking any political tone. "I think this is harder on our families than it is on us because you don't really know what's going on," he told his mother.

Most families were happy to receive word from the hostages, regardless of what the letters said. "At least, you know he's all right. Any time you hear from him it's a good sign," said Phillip Lewis of Homer, Ill., the father of Marine Sgt. Paul E. Lewis, 22.

His son wrote several short letters expressing thanks for the Christmas cards the hostages received. "It is times like these that make me especially proud to be an American," Sgt. Lewis wrote.