Reimbursement is tricky. The employer can reimburse travel expenses tax-free under an accountable plan, but only for "temporary" work-related travel away from your "tax home." So you must have a tax home and the contract must be temporary within the meaning of the regulation. This is also described in IRS publication 463. The employer can pay the travel expenses as an advance, but must reconcile them in a timely manner by collecting receipts and other proof, and obtaining repayment if the actual expenses are less than the advance.
The employer paying living expenses directly is even trickier. Normally, everything of value provided to an employee for their services must be considered part of their taxable income, and that includes free lodging or room and board. The only time an employer can provide room and board that is not taxable is if it is a necessary condition of employment and it is on-site for the job. For example, if you are a live-in nurse for an elderly person and you get free room and board in addition to a salary, the room and board is not included in your wages because living on site is a condition of performing the job. However, if you work in a hospital, and the employer pays for a nearby apartment, that must be included in your wages.
"If the employer pays for your living expenses directly then you would not get the money so it would not be taxable on your return"
Employer paid housing is still taxable and must be included in taxable W-2 wages and subject to withholding unless it is on the employer's premises and accepting the housing is a condition of employment--even if it is not paid to the employee.
