Thirty thousand in credit card debt is a "big elephant to eat" so to speak. But you do it by taking a bite at a time. One positive is that you do not want to borrow from your 401K. Doing so is a horrible idea.
The first question you have to ask yourself and understand, is how you accumulated 30K in credit card debt in the first place? Most people get there by running up a relatively small amount, say 5K, and playing the zero transfer game a few times. Then add in a late payment, and a negative event or two (like the car breaking down or a trip to the emergency room) and poof a large amount of credit card debt.
Obviously, I have no idea if this is how you got there, and providing some insight might help. Also, your age, approximate income, and other debts might also help provide more insight. I assume you are still working and under age 59.5 as you are talking about borrowing from your 401K.
Where I come from is that my wife (then girlfriend) found ourselves under stifling debt a few years ago. When we married, we became very intentional and focused on ridding ourselves of debt and now sit completely debt free (including the house). During our debt payoff time, we lived off of less than 25% of our salary. We both took extra jobs when we were able. Intensity was our key.
If I were you, I would not refi the house. There are costs associated with this and why would you put more debt on your home?
I might cash out the annuity provided that there are no negative tax consequences and depending on how much you can get for it. Numbers are the key here. However, I feel like doing so will not retire this debt.
The first thing you need to do is get on a written budget. A game plan for spending and stick to it. If you are married, your spouse has to be part of this process. The budget has to be fresh each month, and each month you and your wife should meet. To deviate from the budget, you will also need to have a meeting. My wife and I still do this despite being debt free and enjoying very healthy incomes.
Secondly, it is about cutting expenses. Cable: off. No eating out or vacations. Cut back on cell phone plans, only basic clothing. Gift giving is of the $5 variety and only for those very close to you. Forget lattes, etc. Depending on your income I would cut 401K contributions to zero or only up to the company match (if your household income is above 150K/year).
Third, it is about earning more. Ebay, deliver pizzas, cut grass, overtime, whatever.
All extra dollars go to credit card balance reduction. At a minimum, you should find an extra $1000/month; however, I would shoot for 2K. If you can find 2K, you will be done with this in 13 months. I know the math doesn't work out for that, but once you get momentum, you find more.
How good will it feel to be out from under this oppression next March?
I know you can do this without cashing in the annuity or refinancing. Do you believe it?