Suggested answer:
(1) Look at is the expression that is most commonly found in the corpus, while look on is the least common, e.g.
Theresa doesn't even look at Annabelle.
...and not just look on this job as routine.
(2) Look after typically has the meaning of "keep an eye on/take care of", e.g.
...my parents engaged an elderly trained nurse to look after Dermot.
(3) In the following two examples look at and look on can be said to have similar meanings, i.e. both have the meaning of "regard/consider":
...you need to look at this with a little compassion.
...and stood looking on it with joy.
Read about verb + preposition combinations here
Terminology: preposition