I have lost three birds to my cat cause he can jump up and reach in and eat them.

Are there any bird cages which cats can't get to?

There are not, but you can put the bird cage in a room and choose 'lock' ... 'pets'

What about that tree thing (the one without the cage around it?) wouldn't the bird just fly off whenever the cat came around and perch somewhere else?

Unfortunatly, with that bird tree thing the birds can only stick to perching on their's (of what I know, correct me if I'm wrong). But I know they are still in danger of being eaten by a cat.

I do know that with the tree thing,if you have 2 of them in the same room or area outside and only have 1 bird,that the bird will fly back and forth between them.Maybe this will help with your cat situation,but if not,sorry,the only other thing I can think of is,like someone else said,to use lock pets on the door.

well, since the cat actually caught the birds in the first place I suppose it is only fair he got to eat them.