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Steroids like prednisone are known to cause some lethargy. It's one of the reasons why it works for itching. It suppresses the dog's urge to scratch and give them a an overall calmer feeling. It has never been formally studied but in my experience it also can cause some urinary incontinance.
You should start to see this decrease as the days go by.
If not, you can give your vet a call and get a consult over the phone.
Let me know if you still have questions.
I would keep a close eye on him and see the vet if you don't start to see this resolve soon. It's pretty normal to see some changes in behavior for the first few days after your pet starts steroids but it should clear up within a week or so.
Let me know if you have more questions about this.
And thanks for the bonus.