You're mixing up formal charge and oxidation states.
Formal charge:
Number of valence electrons - (Number of lone electrons + 1/2 bonded electrons)
In NHO3 Visualize the structure, N is the center with an H and 3 O's bonded
O...N...O
.....OH
N Valence = 5
O Valence = 6
H Valence = 1
One O is double bonded, One O is single bonded, and OH is single bonded.
Therefore Nitrogen has 4 electrons (8 bonded electrons/2 = 4)
5-4= +1