Step 1: Electron gain enthalpy is NOT always exothermic (exceptions like noble gases, Be, N due to stability). Hence Statement I is incorrect.
Step 2: Ionization always requires energy, so Statement II is correct.
Step 3: Due to half-filled stability of nitrogen (2p$^3$), IE(N) > IE(O), so Statement III is incorrect.
Step 4: Lithium is most electropositive among group I due to small size and high ionization energy, so Statement IV is incorrect.
Step 5: Hence incorrect statements are I, III, IV.