Step 1: Examine each complex.
\[
\mathrm{[Pt(en)_2Cl_2]^{2+}}
\]
shows cis--trans geometrical isomerism, and the cis-form is optically active.
Hence,
\[
\boxed{\text{Both geometrical and optical isomerism}.}
\]
\[
\mathrm{[Co(NH_3)_3(NO_2)_3]}
\]
shows only geometrical (fac--mer) isomerism and does not exhibit optical isomerism.
\[
\mathrm{[Cr(H_2O)_2(C_2O_4)_2]^{-}}
\]
shows cis--trans geometrical isomerism, and the cis-form exists as optical isomers.
Hence,
\[
\boxed{\text{Both geometrical and optical isomerism}.}
\]
\[
\mathrm{[Co(en)_3]Cl_3}
\]
shows only optical isomerism (\(\Delta\) and \(\Lambda\) forms), but no geometrical isomerism.
Step 2: Choose the correct complexes.
Therefore,
\[
\boxed{\text{I and III only}}
\]
exhibit both geometrical and optical isomerism.
Hence, the correct option is
\[
\boxed{(D).}
\]