Abstract Syntax Tree of Pure Lambda Calculus
I would like to know if/how evaluation strategies affect the structure of ASTs, how order of operation is reflected in the AST of an expression


They don't, and it isn't. Evaluation strategies are functions which take ASTs as arguments, and return ASTs (or possibly only normal forms), so you can have different evaluation strategies working on the same AST.


  I think if I could just get some practice with the AST representation of some non-trivial functions in any language, I will be okay.


See e.g. this Stack Overflow question:


data Exp = Var String
             | App Exp Exp
             | Lam String Exp



In the case of pure lambda-calculus, there is no Constant Int, and and would look like

Lam "a" 
  (Lam "b" 
     (App 
        (App 
           (Var "a") 
           (Var "b"))
        (Lam "t" 
           (Lam "f" 
              (Var "f")))))