I am sorry I think we are getting confused. When you said SE I immediately thought Samurai Eddie, not soldier eddie (silly me it's under soldier eddie forum thread). So I was giving advice on Samurai which drops as 5*.
Until you get the materials to take Soldier Eddie to 4 I would use the wicker man Eddie he is your strongest.
your best team right now would be Wickerman Eddie, allied General and Blue allied soldier. If you have the party cost available put the starting Eddie in the second spot since he is lvl 4. You will level him up also and can also use him in a pinch if your wickerman gets low. Also once you get your SE up to 4* use your wickerman ally with him and general.
Most of the other characters you have are going to gathering dust real soon, I wouldn't invest alot in them.