Sponge is a solid. This is because it has a definite volume and a definite shape.
It changes its shape only, when an external force is applied.
We can see that there are several minute or small holes in a sponge.
In these holes, air is trapped. That's why when we press it the air trapped in the holes comes out.
Solids are generally less compressible.
But, in this case, when force is not applied, sponge comes back to its original shape.
Hence, it is considered as a solid.