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Unfortunately, as your Uncle did not have the trust document notarized, it is not going to be effective as a trust.
However, as you are the only heir, you can inherit the property through "intestate succession" (see: http://www.nolo.com/legal-encyclopedia/intestate-succession-california.html) and enter the non-notarized trust as an exhibit into the probate proceedings to help with any issues that may arise (there shouldn't be any).
To transfer the property you have 2 separate things you need to do.
You need to transfer the title to the property, you will do this through the probate court (I would recommend hiring a lawyer to help you with this, as a non-contested probate proceeding this should not take a long period of time, so it should not cost a lot of money, but it is important to do it properly the first time as fixing errors later gets expensive). You can find more about probate court here: http://www.courts.ca.gov/8865.htm
You need to get the mortgage transferred to you - you can do this either by applying with the mortgage company and asking them to transfer the account to you (they may or may not be willing to do this, it depends in a large part on your credit worthiness - credit score, outstanding debt, job history), or you can try to get financing from other lenders (such as credit unions or small banks (good places to start), or a mortgage broker.
In the meantime, it is important to ensure that the mortgage payments stay current, or that you have a written deferrment agreement with the mortgage company (if you are hoping to get them to allow you to take over payments, this is probably not a good strategy, but a deferral agreement is where the mortgage lender agrees to allow you to miss payments, so there is a greater accrual of interest). If you do not make payments or have a written deferral, the property can be foreclosed on.