Is it necessary to reorder nodes (using Reverse Cuthill-Mckee algorithm, for example) if I am already using a CSR or CSC storing technique? Because since CSR/CSC stores only non-zero elements I guess reorder wouldn't be much advantageous.
You should use a reordering. Although it's true that storing a sparse matrix requires the same amount of memory whether or not you reorder it using RCM, reordering it should lead to faster calculations (eg matrix-vector products) due to different/better utilization of cache.
Something to keep in mind is that the "best" reordering depends upon what you intend to do with the matrix. Bandwidth reduction reorderings (like RCM) help with matvec's, but if you're reordering a matrix for parallel distribution you should look into methods that minimize edge-cut/communication-volume (like METIS, others), and if you're looking into sparse direct methods you should consider unstructured nested-dissection (METIS/SCOTCH) or fill-minimization (minimum degree or appproximate MD).