You did not say in what state you and your wife live. That will make a difference here because if you live in a community property state it may need to be handled a bit differently than a non-community property state. You and your wife need to file accurate tax returns and pay the tax that is due for 2015 and going forward. Your wife also needs to file returns for past years, too. Note that filing returns with the IRS will not automatically result in her immigration status being revealed to ICE. Federal tax law prohibits the IRS from making that disclosure. ICE would have to already have reason to believe your wife was illegal and make a specific request for her tax information for the IRS to provide ICE that information. Of course, if ICE already knows or suspects she’s illegal then she’ll have to deal with the immigration issue sooner or later, and failing to file and pay the taxes she owes can work against her in immigration proceedings.
I suggest that she consult an immigration attorney to see about getting a legal immigration status in the U.S. based on your marriage. I suggest that the two of you consult a tax attorney about handling the tax matters. This is one circumstance in which I do not recommend any other type of tax professional (enrolled agent or CPA) because your conversations with those other tax professionals are not covered by the attorney-client privilege and the more limited privilege for tax professionals under federal law does not protect from disclosure any information about criminal matters, which could include illegal immigration.

