Catalyzes the formation of 2'O-methylated cytidine (Cm32), 2'O-methylated uridine (Um32) or 2'O-methylated adenosine (Am32) at position 32 in tRNA. Confers resistance to oxidative stress. cytidine(32) in tRNA + S-adenosyl-L-methionine = 2'-O-methylcytidine(32) in tRNA + H(+) + S-adenosyl-L-homocysteine S-adenosyl-L-methionine + uridine(32) in tRNA = 2'-O-methyluridine(32) in tRNA + H(+) + S-adenosyl-L-homocysteine adenosine(32) in tRNA + S-adenosyl-L-methionine = 2'-O-methyladenosine(32) in tRNA + H(+) + S-adenosyl-L-homocysteine Homodimer. Inactivation of the gene abolishes Cm, Um and Am formation in tRNA. Mutant has increased sensitivity to hydrogen peroxide (H(2)O(2)), with reduced expression of oxyR-recG, katB-ankB, and katE. Belongs to the class IV-like SAM-binding methyltransferase superfamily. RNA methyltransferase TrmH family.