Answer: N = +5, O = -2, H = +1
Each H ion has a positive 1 oxidation state when reacting with nonmetals. Each oxygen generally has a -2 (unless in peroxides). The sum of all the states will be 0, so lets set
H + N + O3 = 0
+1 + N - 2(3) = 0
N = +5
so N = +5, O = -2, H = +1