I could look in the dictionary, but from what I understand from my own language I would say that all three can be used interchangeably, but "cerca" seems to say that there is something inside: a house, a property,...; "valla" makes more reference to a separation between two properties; and "verja" is more something that has a closed/open door. And the dictionary seems to agree somewhat with me: verja Del fr. verge. Enrejado que sirve de puerta, ventana o, especialmente, cerca. valla Del lat. valla, pl. de vallum 'estacada', 'trinchera'. 1. f. Vallado o estacada para defensa. 2. f. Línea o término formado de estacas hincadas en el suelo o de tablas unidas, para cerrar algún sitio o señalarlo. cerca De cercar. Vallado, tapia o muro que se pone alrededor de algún sitio, heredad o casa para su resguardo o división.

I would say that "valla" is the joker word, that could be used in any of the cases. But it usually refers to city walls or fences, like this one: http://www.inmava.com/sites/default/files/styles/colorbox_imagen_producto/public/imagenes/valla_peatonal_dos_patas.jpg?itok=Dg5B7bPa "Cerca" is commonly used for wooden fences for animals or in farms or houses in the wild. Also, those wooden and small fences used to separate the property from another property or the public street. This would be an example: https://thumbs.dreamstime.com/z/cerca-de-madera-32150380.jpg Last, but not least, "verja" is an iron fence or door. It can also refer to entrances similar to this kind of fence. This would be an example: http://domingotorres.com/wp-content/uploads/2011/09/5051-Verja-forja-artistica.jpg Hope this explanation has been helpful :)