Some things that we do know about Odo:
Odo was known to go kayaking with O'Brien, and to read detective novels. Quark also once caught him reading a romance. A speech of Odo's in "A Man Alone" might be interpreted to mean that he liked Karo-Net and Earth jazz. Odo never learned to gamble, and apparently did not care for Klingon opera. He was an adept reader of body language, and never carried a weapon even as part of his job. For the first two seasons, he had no quarters, resting instead in a bucket in the back of his office. Spiritually, he was an agnostic. His blood type, while he was human, was O-negative.
The that name Odo ultimately went by, Odo, was derived from the label on the beaker he firt rested in: "odo'ital", Cardassian for "unknown sample", or, literally, "nothing". Odo was studied by Dr. Mora, who saw to his education, and he tried to fit in by using his shapeshifting abilities to entertain others. Eventually Odo learned to take humanoid form.
After being the main attraction at a reception for the Cardassian High Command, Odo had an argument with Dr. Mora, and left the research center. He apparently spent some time in the mines, where he was often asked to settle disputes among the Bajorans, as he was considered a neutral observer. Then Odo was forced by Gul Dukat to investigate the murder of Vaatrik; his first criminal case. Kira was the prime suspect, but he let her go when she convinced him she was elsewhere committing sabotage at the time. He later discovered that she was responsible.
Odo became chief of security on Terok Nor, and once arrested three Bajorans -- Timor, Ishan, and Jillur -- for an assassination attempt on Gul Dukat. After they were executed, Odo discovered evidence that they had been innocent. He deeply regretted the incident, which probably motivated his dedication to justice above the rule of law. Odo remained as security chief when Starfleet took the station over.