Method: Compare using known aqueous pKb values. Ethylamine pKb ~3.3, diethylamine ~3.0, triethylamine ~3.3-3.4. A lower pKb means a stronger base. Diethylamine has the lowest pKb, so it is strongest, followed by triethylamine, with ethylamine weakest. Diethylamine's conjugate acid keeps one N-H for hydrogen bonding while enjoying a solid +I effect. Triethylamine loses the N-H bond entirely, so its conjugate acid is poorly solvated. Ethylamine keeps two N-H bonds but has only a single ethyl group's +I effect. Ranking: diethylamine, triethylamine, ethylamine, II > III > I.
\[\boxed{\text{II} > \text{III} > \text{I}}\]