find a path to visit every node in graph not necessarily once
You probably haven't found anything in your searches because this problem is fairly easy to solve, without needing any fancy methods.
If the graph is strongly connected, then it is easy.  Let $s$ be the starting node.  Pick any vertex $v$ you haven't visited yet, and append a path $s \leadsto v$ followed by some path $v \leadsto s$ (both must exist, since the graph is strongly connected).  Repeat, appending to the end of the path, until every vertex has been visited.
If the graph isn't strongly connected, decompose it into a dag of scc's.  Then you can reduce the problem to finding a path through this dag (within a scc, use the algorithm of the first paragraph).  You can find a path to visit every node in a dag iff the dag is itself a path, i.e., it has the structure $v_1 \to v_2 \to \dots \to v_k$, and then it is trivial to write down this path.
This is not a Hamiltonian path, since it may visit the same vertex multiple times.