If I was recently laid off from a job out of state and left quite a few personal belongings, is my former employer in charge of shipping?

Generally speaking, no.  Employees are usually responsible for their own relocation expenses-- even when the termination was insisted upon by the employer.  Even though this is a general rule, there are exceptions in the form of employment conditions, relo agreements, or company policies.  A few companies do assist with relo expenses and will not want to be liable for any of your belongs which were left behind.  If you had an agreement that provided for post-termination relocation expenses or your employer had a policy to provide assistance with these expenses, they you invoke those provisions.  If you're not sure, contact your former HR manager (or the functional equivalent), and see if any of these options are available for you.