If you look at the info shown at the top of your window, your scene has 40 million vertices, that is why things are slow.
You probably had a subsurf on one object but when you joined them together the subsurf then became active on the new denser mesh.
As you have a subsurf division setting of 4, that means you have about 150,000 real vertices or 25,000 vertices in each original object. With the subsurf at 4 divisions on only one of them, you would have had 6.8 million vertices before joining. That jump from 6.8 million to 40 million will be the reason for the performance difference.
A subdivision setting of 4 is high, dropping it to 2 will give a similar visual result with only 2.5 million vertices.
From what I can see of your object, 157,000 vertices for each item is extremely high. I would expect to use less than 200 vertices for a shape like that. Adding a subsurf with a division of 4 on 6 of the lower poly objects would leave you at about 300,000 vertices which will be very fast to work with.