Best approach to copy multiple objects to other levels?

There are 2 ways to move the assets tself. Either using “migrate” or copy the files through the windows file browser.
With migrate, you would need your static meshes etc. correctly setup, See here for further information:

For copying, you can just use Ctrl+C and Ctrl+V as long as the meshes are in the same folders in the content browser.
So you select your objects in your level, copy and paste them over. Try 1-2 objects at first and see if the staticmesh actors have a static mesh assigned to them, if not they will be an empty actor and you have to reassign the static mesh through the Details Panel.