Step 1: In aqueous solution, basicity of amines depends on three factors: electron donation by alkyl groups (+I effect increases basicity), steric hindrance around nitrogen, and hydrogen bonding of the protonated ammonium ion with water.
Step 2: A primary amine like ethylamine has only one alkyl group, so the +I effect is weak, though it has two N-H bonds available for solvation.
Step 3: A secondary amine like diethylamine has two alkyl groups giving a stronger +I effect, moderate steric bulk, and still one N-H bond left for hydrogen bonding, so it is the most basic of the three in water.
Step 4: A tertiary amine like triethylamine has the strongest +I effect but no N-H bond and suffers the most steric hindrance, lowering its basicity below the secondary amine but still above the primary amine.
Step 5: The observed order of basicity in water is diethylamine > triethylamine > ethylamine, that is, II > III > I.
\[\boxed{\text{II} > \text{III} > \text{I}}\]