You can withdraw contributions from the Roth immediately. To withdraw earnings, you must have the Roth open for 5 years.
But somehow, the idea of paying a big chunk of taxes to convert from a traditional IRA or 401K to a Roth, and then take out money to buy a house, doesn't make a lot of financial sense. You have not planned very well, over-contributing to your retirement and not saving enough outside of it. You should have an expert run the numbers for you and see if you have enough years left to recoup what you are losing to taxes. If it still makes sense to do the conversion, then you can withdraw contributions to the Roth plan for the house.