Step 1: Recall the molecular structures of nitrogen oxides.
Nitrous oxide,
\[
\boxed{\mathrm{N_2O}},
\]
has the linear structure
\[
\boxed{\mathrm{N-N-O}.}
\]
The remaining oxides,
\[
\mathrm{N_2O_3,\ N_2O_4,\ N_2O_5},
\]
are not linear molecules.
Step 2: Choose the correct option.
Therefore,
\[
\boxed{\mathrm{N_2O}}
\]
is the oxide of nitrogen having a linear structure.
Hence, the correct option is \(\boxed{(C)}\).