Wobbling on Shimano Nexus 8
You likely need to tighten the hub bearings.  I'd take it to a shop and ask for a hub bearing adjustment.  

On most hubs I'd say you can do it yourself but the Nexus series are complicated and have different features depending on the model.
This means most step-by-step directions for standard hubs won't apply.  E.g. it may have a brake built into it.

You're better off paying an expert to do it IMHO.