This information is given for educational purposes only. No attorney-client relationship exists between us.
From what you have written, it appears your husband appeared for trial without an attorney and Dodeka got a judgment. The writ of execution means the court has given them the right to find and seize whatever assets your husband may have to satisfy the judgment. The notice of deposition means they intend to take your husband's sworn testimony and have asked him bring certain documents, probably bank statements. As for the Request for Admissions, I don't know what is asked in this case, but DO NOT FAIL TO ANSWER. You really need an attorney to help you with those because failure to answer or improper answers will really hurt.
Keep in mind that Texas is an extremely debtor friendly state. Nobody gets your house except the bank and the IRS. Nobody gets your car except the lender and the IRS. Nobody gets your wages except the IRS and child support. Nobody gets your pension/retirement except the IRS. Most people don't have any thing more than that, so there is nothing to get to satisfy a judgment. HOWEVER, a judgment is good for 10 years and can be renewed. The creditor is hoping that one day you will have some money saved a large credit purchase (car or house). When you apply for that loan, the judgment creditor will learn you have cash and will then try again to get you to pay.
You really need an attorney to help you resolve this matter. I offer free initial consultation.