Step 1: What makes a strong base.
An amine is a stronger base if its nitrogen can hold a proton well. More electron push onto the nitrogen helps it grab a proton.
Step 2: Two effects to balance.
In water, two things matter. One is the electron push from alkyl groups. The other is how well the formed positive ion is steadied by water through hydrogen bonds.
Step 3: Why aniline is weakest.
In aniline the nitrogen lone pair is pulled into the benzene ring. This leaves less push on nitrogen, so aniline is the weakest base here.
Step 4: Compare the alkyl amines.
Trimethylamine has three methyl groups, but they crowd the nitrogen and block water from steadying the ion. So it is less basic in water than expected.
Step 5: Find the winner.
In water the order works out as dimethylamine first, then methylamine, then trimethylamine, then aniline. So the secondary amine wins.
Step 6: Final choice.
So in water the strongest base is dimethylamine.\[ \boxed{\text{Dimethylamine}} \]