Yes, the IRS does recognize their role as non-profit volunteers and I'll list some of what they can deduct from their taxable income. They can choose between deducting gas/oil used or mileage. If they don't have their own transportation they can deduct subway, bus, or taxi fare. They can also deduct food and uniform cost, and other expenses they incur and out-of-pocket costs while volunteering.

You can deduct mileage for charitable purposes, currently .14 per mile (this rate can change annually), other travel expenses including meals, uniforms, and any other out of pocket expenses that are directly related to the non-profit. Keep in mind the non=profit has to be a charitable organization under IRS rules and these are itemized deductions, so you have to itemize to take advantage of them.

If the non-profit pays for their expenses, these can be no tax expenses. What you could do is, create a "volunteer fund" and encourage a sponsor to match the donations into the fund, made by the volunteers and supporters of the organization. Provide all donors (volunteers included) with a letter of acknowledgement for their donations (tax deductible). Then, use these funds to pay for their expenses, tax free.