I recently had a judgment against me and got served a notice of Judgement. I have a bank account that is in myself and my boyfriends name. My question is: can they legally take money out of this account or freeze and take my boyfriends money that he deposits on there if we are not married? And if they can, what can I do?

Short answer YES, He will have to file a Motion with the court to quash the garnishment on the account. He will have to convince the court that x-amount of dollars is his only, he must be able to document the money.
contact an attorney.

Thank you for your quick answer, I think what I might do is have him taken off our joint account and he can open his own account before they put a freeze on it and something, that way they can't touch his money.

Also does anyone know if this judgement can affect my tax return? Can they take that and use it toward my debt?

If the a levy the account you will not be able to remove any money from it. If the have not attachted yet then remove all but 5.00, have him open a new account in his name.

Yes, There is many ways we can get the money from the Judgment, one of them is your income tax. There is No limit. If you own it, It can be taken.