Rep. Christopher J. Dodd, 36, is one of the Senate's two new Democrats.

He moved up easily to the body that censured his father, Thomas J. Dodd, in 1967, for misuse of campaign funds. Dodd ran on a campaign to unify the state party after a badly divisive presidential primary season and is widely regarded as a major new figure in the state.

The handsome, relaxed young attorney was one of the post-Watergate flood of Democrats who came to Congress in 1974, and he built his reputation for easy-going accessibility with town meetings and a mobile office, winning reelection in 1978 with 70 percent of the vote. While he supports more defense spending, Dodd considers himself a moderate liberal who opposes the MX missile and the B1 bomber.

He was backed by labor against former New York senator James L. Buckley, a Republican whom Dodd called an overly conservative carpetbagger, "a second-hand rose." A member of the House Rules Committee, Dodd has an interest in energy matters and has boosted conservation and alternative energy sources. He supports the Equal Rights Amendment and voted for federal funding of abortions although he is personally opposed to abortions. He was a Peace Corps volunteer in the Dominican Republic from 1966 to 1968. Illinois

Alan J. Dixon, 53, maintained his undefeated record from 30 years of Illinois politics this week by topping Republican Lt. Gov. Dave O'Neal to succeed retiring Sen. Adlai Stevenson. He is one of two new Democrats in the 1980 freshman Senate class.

After beginning his career as a police magistrate in his hometown of Belleville, where he still lives, Dixon was a state legislator and then Illinois secretary of state for two terms, leading the Democratic ticket both times. An attorney, he got off to a rocky start in his run for the Senate with a botched news conference, but worked hard to beef up his knowledge of national and international affairs to counter any impression that he was too parochial for statewide office.

He called for passage of the Equal Rights Amendment, higher defense spending, more benefits for senior citizens and new incentives for investment to state banks, and his campaign had the strong backing of the Illinois Democratic machine and Chicago Mayor Jane Byrne. Dixon's stands seemed to spark some movement toward the middle of the political spectrum by O'Neal, who grew up and also still lives in Belleville. The father of three, Dixon likes to play golf in his off hours. b