Combine graham cracker crumbs, melted butter, cinnamon, and nutmeg in a bowl.
Press the mixture into an 8-inch pie dish; refrigerate while making the filling.
Beat cream cheese in a mixing bowl with an electric mixer on medium speed until softened.
Reduce speed to slow; gradually beat in milk (the mixture will be watery).
Use a rubber spatula to scrape cream cheese from the sides of the bowl, if necessary. Beat in pudding mix until the filling is thick and smooth.
Spoon 1/2 of the cream cheese filling onto the bottom of prepared crust. Spread 1/2 of the strawberries over the filling; repeat with remaining filling and strawberries.
Chill pie in refrigerator until filling is set, at least 1 hour.