It seems there are different versions of that first one. The way we used to sing it was
My name is elli elli, chickali chilali, ooly ooly up up up. Jump in a lake and swallow a snake and come out with a belly ache (at which point you try and pole each other in the belly without getting poked).

I think this was my favourite growing up
Down by the banks of the hanky panky, where the bullfrogs jump from bank to banky with a hop, hop, rattle and a pop (again you'd try and poke each other without getting poked)

Now I'm kinda hoping this baby is a girl, just so I can do these with her when she's a bit older (boys always seemed to be far too cool for this)