The biggest problem with what I have you are proposing (using your equity to pay off other debt) is that it doesn’t seem like you asked yourself (a) how you got into the other debt to begin with and (b) what are you going to do differently so that you don’t repeat that again if you do decide to sell your home and use the money to pay off your debt.

Imho,

1) I would take option#1 and live as frugally as you can.
2) Option#2 would be something I think you should NEVER do. I would NOT turn your home into a piggie bank and take out a HELOC to pay off other debt that doesn’t generate incoem. All you’ve done is just shift your debt elsewhere to something that a creditor can go after: your primary home.
3)Option#3: you’ll still need a place to live, and you probably should figure out how much rent cost will be, versus how much your monthly mortgage+property tax+insurance/etc is less tax deduction.

Do not get excited about the equity in your primary home. Otherwise you run the risk of being exactly like the other americans during the earlier real estate meltdown when they decided to atm their home to death…That is, unless you don’t mind selling your home to people like me looking to buy a distressed property going through short sales.

Pretend the equity doesn’t exist, and make your financial plan accordingly.