Is it legal for a credit card company (Sears) to garnish your wages? And have access to your bank account? i.e to know when and how much money you deposite in your checking account.

Absolutely! Yes, it sounds crazy, but it's perfectly legal. Highly unethical, but very legal. The best option for you now (in my opinion) is to call Sears and make some kind of payment arrangement and get something IN WRITING saying that they will stop the garnishment. After you have that, close the checking account that which they have access, and send the payments in the form of money orders from now on. Never ever ever let a creditor get hold of your checking account number!!

It's only legal because you gave Sears your account #. All you have to do is change your bank and NEVER let anyone access to it.

IF they've obtained a judgement against you, then yes.