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.