Atlanta tax expert,

I submitted my wife's W7 and my 1040 EZ form. However I forgot to attach my W2 form along with my 1040 EZ. What should I do now. Will they reject my tax forms. I would really appreciate a response. Thanks.

I believe the IRS has a copy of the W-2.
They may send you a letter asking for a copy.

Normally IRS accepts returns as filed unless there is some mistake in the return. So there should not be any problem.
You have file W-7 so it will be processed before your return is processed. By that time, IRS will have all your W2 and 1099 (if any).

Can you please tell how when should I expect to see a refund in my bank account. I have selected the direct deposit option. Thanks.

If you efiled, probably 10-14 days.

If you mailed the return, about 6 weeks.