He does decent enough. He certainly won't be killed or anything, but in terms of actually solving crimes and detective work, he won't do so well on his own and will need to heavily rely on the likes of his allies.
In terms of stopping the various super criminals and busting up gangs and whatnot, Thor will bash people's faces in. He'll likely be intimidating, but won't have the fear advantage Batman does.
Thor is awfully heavy. I'd imagine that he'd have trouble doing anything if he were powerless. But for the sake of this thread, let's pretend that he had at the very least olympic level speed and agility, not very many Batman opponents would be able to go toe to toe with him based on the tremendous strength that a man of his weight could bring to a fight. Thor is nearly twice the weight of the Kingpin.
The actual fighting won't be the problem.
Bruce is Bruce because he is smart and savvy as heck. This will not bode well for Odinson's brand of superheroing.
He may not be Bruce but he's not dumb and can adapt thats why he has the other team members. Henry Russo is a smart hacker that beat Microhip in hacking a guy that could hack into the X-mens (Reavers) computer for fun. He can also hack into sattelites. It's also partially due to Henrys tactics that Norman Osborn brought in The Hood.
Falcon can also telepathically to any bird and see through their eyes. Er you know who Black Widow is right. Y'know the superspy? Then we geot Silver Sable.
I will say this finding people and getting information isn't going to be a problem.
__________________ Watch what people are cynical about, and one can often discover what they lack.
- General George Patton Jr
Since you put it that way, I guess it could work. I thought you had him as being the brains of the crew. If he's mainly the point man and the muscle, then yeah it could work.
Does he have access to Shield tech?
I think you're narrowing it down into a specific criteria. I've already gone into some of the stuff the team can do. For starters I think you're exaggeratting how smart The Riddler is, maybe he has some recent showings that are really impressive but for most part of his career he has been a street level villain. Robin has been able to easily outsmart him.
Black Widow has been able to outsmart an AI system that had fooled the whole of SHIELD and was going to take it over. Henry Russo was instrumental in helping punsiher fight The Hood and Norman Osborn.
I didn't realise this but unfortunately looks like I'm going to have to bring up Norman Osborn again. Norman Osborn isn't a street level supervillian anymore. I know you might think that he only got power in Dark Reign through sheer luck and shown scans with Norman Osborn saying so but it doesn't matter. If somebody says something on panel but the reality of the comic contradicts it doesn't matter. It's like Martian manhunter saying that Aquaman has no psionic powers but in the page before he uses TP. Obvioulsy luck was involved in him getting that power but he still had to be highly intelligent to utilize it and that's proved by the fact that Norman helped come up with a plan to save Doom's life. Y'know you have to be highly intelligent to save his life.
They basically have access to what is in a standard Shield hellicarrier. However any other tech they have to get through other means.
__________________ Watch what people are cynical about, and one can often discover what they lack.
- General George Patton Jr