I will enter Texas on immigrant visa, my wife is US citizen and she is unemployed for the last 2 years,how should I deal with the Taxes Authorities?
Your status with respect to federal income tax depends on when you enter the US and on your presence during the previous two tax years (because of the substantial presence test). See Determining Alien Tax Status and Alien Residency - Green Card Test on the IRS website. From the latter:
If you meet the green card test at anytime [sic] during the calendar year, but do not meet the substantial presence test for that year, your residency starting date is the first day on which you are present in the United States as a Lawful Permanent Resident. However, an alien who has been present in the United States at any time during a calendar year as a Lawful Permanent Resident may choose to be treated as a resident alien for the entire calendar year.
From the former:
You can be both a nonresident alien and a resident alien during the same tax year. This usually occurs in the year you arrive or depart from the United States. If so, you may elect to be treated as a Dual Status Alien for this taxable year and a Resident Alien for the next taxable year if you meet certain tests. (Refer to section "Dual-Status Aliens" – "First Year Choice" in Publication 519, U.S. Tax Guide for Aliens.)
(I don't know anything about taxation in Texas, but similar considerations probably apply.)