Does anyone know anything about this glue? I never heard about it before but this girl used it for a platform perch.

http://ambermuffinz.blogspot.co.uk/2012/08/super-easy-platform-perch.html

I have dozens of those popsicle sticks and I was thinking of doing something similar, but knowing that glue is a big no no I need to know if this White Elmers glue is really non-toxic

It's nontoxic. It's frequently used by children in the US and some of them actually like to eat it, so it has to be safe to avoid poisoning the kids.

There are other brands of nontoxic glue that would be bird-safe too. The big risk with glues is the fumes, more than the toxicity of the glue itself. Elmers glue doesn't have fumes, but the 'household cement' type of glue is usually hazardous to birds and shouldn't be used around them.

Thank you Tielfan.
Would this one be ok?

http://www.amazon.co.uk/WOOD-WORKING-SUPER-STRONG-TOXIC120G/dp/B004TXJH9Y/ref=sr_1_1?ie=UTF8&qid=1389221757&sr=8-1&keywords=non+toxic+wood+glue

I have found a few Elmer's as well but the idea of spending £5 which is about $8 for a bit of glue revolts me.

Also, when they say "washable", what that means? that you can wash it off your hands if you make a mess, or that if you wash the part you glued it will come off? Sorry it sounds a very daft question but I am not sure.

Elmers glue washes away when it gets wet. So you only want to use it on things that are expected to stay dry.

Apparently there are a variety of opinions about the safety of PVA glue (aka white glue). Some say it's non-toxic and others say it's toxic if you eat it. They couldn't legally say nontoxic on the label if it was dangerous to eat it, so I'd say follow the label. Maybe some types can be toxic depending on the formula and others are safe. I''m sure you don't want it to turn into bird food anyway and will be using the glue in places where questing beaks have a hard time reaching it .

Elmers glue is PVA with other things added to it. The internet also says that PVA glue doesn't emit any toxic fumes.

Yes absolutely, I would only glue parts that will be covered and not reachable.
So basically the one in the link should be ok, it says
WOOD GLUE PVA FAST WORKING SUPER STRONG NON TOXIC
What I don't understand about the fumes is, do the glue emits them even after it's dry? If that's so, it can't be safe for humans either.
A glue that dissolves when in contact with water is quite useless for a bird toy. This stuff needs to be washed and scraped regularly for poo, how people manage to keep the toy all in one pieces is something I can't understand.
If the glue in the link isn't good, I guess I will have to find another way to fasten the popsicle sticks to the perch.

Glue fumes are only a problem before the glue has dried. Once it dries the fumes go away.

Elmers glue melts when it's wet but other types of PVA glue can be tougher. I have some PVA glue for jewelry and crafts that is strong and waterproof when it's dry.