I notice that my second-hand Nexus 7 hub - model SG-7R50 (printed on the hub) does not freewheel much at all.

Furthermore if I pedal backwards the wheel starts turning backwards as well - I don't believe that this is a coaster brake model.

Would this be a symptom of a faulty hub? Would an oil replacement fix the problem?

The problem may be internal, but it could also be gunk rust or build up between the cog and the dust cover.Start by taking off the cassette joint and cog and rule out the simple stuff first. If that's all clean and obstruction free, then it might be time to start looking internally.

Thanks. I'll try that first and report back if there's an improvement.

I disassembled the wheel from the bike and removed everything upto and including the sprocket and shield just behind it. There was some gunk back there which I cleaned up.

At this point I tried spinning the wheel whilst holding the axle tight in my hands. It spun reasonably well, much better than when it was installed on the bike.

I refit everything and tried spinning it again, but now it seemed that the resistance was back to what it was before.

Could the problem be caused by the gear cassette mechanism somehow slowing down the wheel?

Before refitting I cleaned up everything with a piece of cloth. However I did not apply any oil or grease on any of the items. Would doing this make a difference?

Sometimes the steel shield or cover behind the sprocket is dented or slightly buckled and engages with the rubber seal behind it, causing the hub to put power back into the sprocket and chain when in freewheel mode.

For this situation what would be the best way to deal with the problem? Replace the shield? Would it be possible do without it?

Take the shield off and examine it. You cannot leave it out as it also acts as a sprocket spacer. If you leave it out the sprocket cannot be fasten securely with the clip. It will have some play, eventually destroying the sprocket driver notches.

I would take the hub apart, at least as far as removing the inner assembly from the shell and see if it is severely gunked up. You need to verify if anything is damaged/worn beyond repair.

Noted about the shield. Though I did come across a youtube video where a larger sprocket with shield is replaced with a 14T sprocket without. Not really sure how that works. I'll post it up if I find it again.

If I remove the inner assembly would I need to worry about spilling/losing grease? I do not have any of that Shimano recommended grease on me. I only have some generic stuff that's red colour that a local LBS gave me for real cheap.

Given that the wheel spun pretty easily minus reinstalling the shield, sprocket and gear cassette mechanism, would not the problem be something to do with these items instead of the internals?

Chances are it's the shield or cassette mechanism, but I would check if the bearings are properly adjusted. Since removing the inner assembly is only two steps more than adjusting the bearing cone on the brake side, I would pop out the inner assembly just to have a look. No grease will fall out.

It's unrelated to the issue you are having (most likely), but after years of use the inner assembly gunks up and the left and right-hand bearings run almost dry. It's not much effort to clean the assembly (at least superficially) without taking it apart, clean the bearing races in the hub shell and repack with bearing grease (any generic bearing grease will do).

If there is a problem with the assembly itself you will likely notice when you take it out. Maybe a pawl has broken or one of the bearing retainers. Clean the big rubber seal as it has a tendency to collect lots of gunk. Lightly oil before reassembly.

I'm having some difficulty removing the inner assembly from the shell.

I'm referring to this video here and have reached the 2mins 47second mark:

https://youtu.be/Dz-3PfboKTw?t=2m47s

I've removed the large rubber shield and exposed the bearings race.

However from this point forward I am not sure how to proceed. The inner assembly does not drop out.

Do I need to loosen anything on the non-drive side?

Any suggestions at all on this problem?