Step 1: Concept Paramagnetic species possess at least one unpaired electron.
Step 2: Meaning Use molecular orbital theory or electron counting. Species with an odd number of total electrons are always paramagnetic.
Step 3: Analysis A. $O_{2}^{2-}$ (18e): Diamagnetic. B. $NO^{+}$ (14e): Diamagnetic. C. $O_{2}$ (16e): Paramagnetic (2 unpaired electrons in $\pi^{*}$). D. $CO^{+}$ (13e): Paramagnetic (odd electron). E. NO (15e): Paramagnetic (odd electron).
Step 4: Conclusion Species C, D, and E are paramagnetic.
Final Answer: (C)