Can they take my last two paychecks?

1) Since you signed a contract stating that you would have to repay $4,000 if you left within one year of the contract date and you are, if we understand the timeline right, leaving within one month, you do owe them the money: you contractually agreed to pay it under these circumstances. That it leaves your family with no money is not relevant: the employer is no responsible for how you budget, your lack of savings, etc. All that is relevant for this purpose is that you agreed contractually to reimburse them $4,000 if you left work within a certain time frame. 
2) However, the employer may not simply withhold money from your paychecks without your consent or without a court order for wage garnishment: the law is very clear about that. Even when an employee owes the employer money, the employer cannot keep his pay. Rather, if you owe them money and won't repay them, they'd have to sue you for the money.
You can file a complaint with the state department of labor and/or sue the employer for the withheld pay. However, neither option will get you the money immediately, and if you do this, they will likely sue you for the money you owe them, too, so that at the end of the day, so to speak, you will still have to pay the $4,000. Since you will likely not come out financially ahead and since you won't be able to get the money now (complaints and suits both take time) when you need it, it may be best to let them keep the money they have already taken, rather then engage in legal actions that won't help you during this time of financial crises. As for the extra $800, send them an offer to repay that when you can; if they refuse to wait, they can try suing you for the $800, if they deem it worthwhile (which they may not, since it's only $800 and they'll already have the bulk of what they want), which will take them several weeks to a few months (depending on how fast they move and how fast your local courts move).