As others mentioned, your employer can reimburse you tax-free for travel expenses if you travel away from your tax home for a temporary assignment, and the employer uses an accountable plan.
Travel means you travel far enough away from your tax home that an overnight (or longer) stay is reasonable.
Tax home is the general area (city, county, etc.) where you do most of your work and earn most of your money.
Temporary means the assignment is expected to last, and actually does last, 1 year or less. If the assignment is indefinite (no expected end date) then it is not considered a tax-free travel expense even if the assignment ends up lasting less than a year.
An accountable plan means your employer tracks your travel expenses and only reimburses you for legitimate travel expenses for your temporary assignment. They can use a fixed per diem, as long as it is not more than the federal reimbursement rate for the area you are traveling to. They can reimburse less than your actual expenses, and up to your actual expenses (or up to the federal per diem), but if they reimburse more, the difference is taxable income.
If you are not traveling on a temporary assignment for this employer, then both you and the employer are tax cheats. Everything paid to you for your work is considered wages and should be included on your W-2 and subject to all income, social security and medicaid taxes (unless you have a legal tax-free employee benefit like medical insurance and a few other things). Your employer is cheating you out of social security contributions that add to your future benefits, and they may be cheating you out of other benefits such as unemployment insurance, workers comp, family and medical leave, or other benefits required by state law. Your employer is also helping you avoid income tax on the "reimbursement" that you should be paying. Both you and the employer would be vulnerable in case this arrangement is discovered.
Thank you for asking about this and for being honest. It seems to me there are enough job openings that you could find a job with an honest employer. If they are cheating on their taxes, you don't know what else they might be doing.
