Can common law override statute law?

Yes and no. In general, in the U.S., a statute overrides pre-existing common law, to the extent of the statute's language. For example, a common law rule may apply to "all contracts". If the legislature later enacts a statute that is stated to apply to "all contracts for the sale of goods," then the statute overrides common law, but only with respect to contracts for the sale of goods.

However, a later court case may arise where there is some question to whether the statute applies as written; there is an issue that is not explicitly covered by the statute (for example, the statute may not have defined "goods"). The court may then interpret the statute's unexpressed terms, and in that sense "override" the statute (at least in part) by its interpretation. And that interpretation will be followed in lower court cases.

But the right of courts to throw out, or void, statutes because they are unconstitutional is well enshrined in U.S. common law.