My company relocated me, and paid for my moving expenses. Since they paid these expenses, are they tax deductible?

My company provided me with a full detailed list of all expenses they provided for my relocation package.  All of these expenses were reported in box 1 of my W2 - nothing was reported in box 12 with a P.  Some of my expenses I paid taxes on - but others, such as lodging and shipping my belongings, I did not.  Can I claim the cost of lodging and shipping those belongings?