President Reagan yesterday nominated Arlington prosecutor Henry E. Hudson to the post of U.S. attorney for the Eastern District of Virginia, an office buffeted in recent years by accusations of weak leadership and disorganization.

Hudson, a 38-year-old conservative Republican who heads a national commission on pornography, would succeed Elsie L. Munsell, who resigned in November after an often rocky four-year term in the office that oversees federal prosecutors in Alexandria, Richmond and Norfolk.

A spokesman for the Justice Department said Hudson's nomination is expected to clear the Senate Judiciary Committee without difficulty and win easy approval by the full Senate shortly after it reconvenes April 8.

Once confirmed in the $70,500-a-year post, Hudson is expected to begin what some close to him say will be a "house-cleaning" of the 76-member U.S. attorney's office aimed at repairing its damaged reputation. During Munsell's tenure, the office became involved in a prolonged controversy about Navy shipbuilding contracts at Newport News Shipbuilding and Dry Dock Co., Virginia's largest private employer, and in a losing criminal prosecution of two of Portsmouth's top political officeholders.

Hudson declined to confirm reports of a pending shake-up. "Initially, I want to take a look at the present organization of the office and see if any changes are necessary," he said. "Until I have a chance to consult with the Justice Department and the members of the staff in the office, I don't want to publicize my thoughts."

The former assistant federal prosecutor said he plans to "put a greater emphasis on the magistrate's court, and cases involving espionage and national significance will obviously be of highest priority."

As Arlington's commonwealth's attorney since 1979, Hudson has been a popular if sometimes controversial public figure. He has earned a reputation as a "policeman's prosecutor" who is a relentless foe of massage parlors and adult bookstores.

His hard-nosed stands on tough jail sentences and plea bargains also have drawn praise from many residents and criticism from defense attorneys who complain he is too rigid.

Hudson was recommended to the president by Sen. Paul S. Trible Jr. (R-Va.) and his nomination came as no surprise. Candidates have already begun jockeying for his Arlington job.

Arlington's Circuit Court judges, who are appointed by the state's Democratic legislature, will name an interim county prosecutor until next November's election. Leading candidates for the appointment are Democrats Helen Fahey, Hudson's chief deputy, and Brendan Feeley, who ran against Hudson in 1983. Assistant prosecutor Liam O'Grady also has been prominently mentioned but is not considered a likely appointee because he is a Republican.