I am developing a scientific application used to perform physical simulations. The algorithms used are O(n3), so for a large set of data it takes a very long time to process.
How optimized are your algorithms? Are you using native BLAS libraries? You can get about an order of magnitude performance gain by switching from naive libraries to optimized ones. Some, like ATLAS will also automatically spread the calculations over multiple CPUs on a system, so that covers bullet 1 automatically.
AFAIK clusters usually aren't treated as a single entity. They are usually treated as separate nodes and programmed with stuff like MPI and SCALAPACK to distribute the elements of matrices onto multiple nodes. This doesn't really help you all that much if your data set fits in memory on one node anyways.