No, these algorithms are impractical, but their utility is in shedding more light on the matrix multiplication problem. So it enables further study, which could lead to more practical advances.
Yes, Strassen is straightforward to implement and makes a huge difference. Another practical algorithm applicable over small Galois fields is the "method of the four Russions" (none of whom are Russian). It's often used as a basecase for Strassen when multiplying matrices over GF2, which has a number of applications in the real world, including crypto research.
