Can I offset my moving expenses with the EI taxable payments received at new location when moving from Alberta to Ontario?"

No, you can only claim Moving Expenses against income "earned" at the new location, and EI does not qualify as earned income.

CRA can disallow a moving expense claim if you didn't specifically move to go to school or for a new job. They consider a move to look for a better job to be personal and therefore the moving expense deduction is not valid.