I was never served an Unlawful Detainer yet my old Landlord file a case and won a Judgement by Default, by law I am entitled to "be served" and I was not. Now I need a sample of how to write a "Motion to Vacate Default Judgement" .

First, where are you located. Second, an Unlawful Detainer is used to evict a tenant when they refuse to vacate. Since you specify an "old" landlord, that seems to indicate you are no longer living on his property. Therefore an unlawful detainer makes no sense and would be moot anyway.

Also, an unlawful detainer doesn't involve a "judgment". It results in a legal eviction order. So, again, if you are already out, its moot.

So something is not right here and you need to determine exactly what the judgment was for.