I work for a National company, with work centers in every province. I work from home. I moved from West to East and am closer to the Toronto office. Can I claim move?

You need to have moved more than 40km to be closer to work to be eligible for a moving expenses claim. If you work from home, it doesn't sound like you moved to be closer to work...

Moving expenses are one of the credits that the CRA tends to scrutinize; It might be a good idea to give them a call to confirm if they'd consider you eligible.

https://www.canada.ca/en/revenue-agency/corporate/contact-information/telephone-numbers.html