You would never report income received as being report on Form W-2 unless it actually came on a W-2.
You don't state whether or not you are clergy. The excerpt below is from the IRS for non-clergy.
Lodging on Your Business Premises
You can exclude the value of lodging you furnish to an
employee from the employee's wages if it meets the following
tests.
- It is furnished on your business premises
- It is furnished for your convenience.
- The employee must accept it as a condition of employment.
Different tests may apply to lodging furnished by educational
institutions. See section 119(d) of the Internal Revenue
Code for details.
If you allow your employee to choose to receive additional
pay instead of lodging, then the lodging, if chosen,
isn’t excluded. The exclusion also doesn't apply to cash
allowances for lodging.
On your business premises. For this exclusion, your
business premises is generally your employee's place of
work. For example, if you're a household employer, then
lodging furnished in your home to a household employee
would be considered lodging furnished on your business
premises. For special rules that apply to lodging furnished
in a camp located in a foreign country, see section 119(c)
of the Internal Revenue Code and its regulations.
For your convenience. Whether or not you furnish
lodging for your convenience as an employer depends on
all the facts and circumstances. You furnish the lodging to
your employee because they need to live on your business premises to be
able to properly perform their duties. Examples include
employees who must be available at all times and employees
who couldn't perform their required duties without being
furnished the lodging.
It doesn't matter whether you must furnish the lodging
as pay under the terms of an employment contract or a
law fixing the terms of employment.
Example of qualifying lodging. You employ Sam at
a construction project at a remote job site in Alaska. Due
to the inaccessibility of facilities for the employees who
are working at the job site to obtain lodging and the prevailing
weather conditions, you furnish lodging to your employees
at the construction site in order to carry on the
construction project. You require that your employees accept
the lodging as a condition of their employment. You
may exclude the lodging that you provide from Sam's wages.
Additionally, since sufficient eating facilities aren’t
available near your place of employment, you may also
exclude meals you provide to Sam from his wages, as discussed
under Meals on Your Business Premises, later in
this section.
Example of non-qualifying lodging. A hospital gives
Joan, an employee of the hospital, the choice of living at
the hospital free of charge or living elsewhere and receiving
a cash allowance in addition to her regular salary. If
Joan chooses to live at the hospital, the hospital can't exclude
the value of the lodging from her wages because
she isn't required to live at the hospital to properly perform
the duties of her employment.
