Hi Jim,
Eraser tools are normally used in bitmap-oriented editors, like Photoshop. Visio is a vector based drawing program, so you would want to delete vertices, lines and shapes.
If you grab the pencil or line tool, you can select paths and delete individual vertexes.
If you click on paths, you can delete them, and you can Shift+click to select multiple paths. Or you can draw a net around a whole bunch of shapes to select, then delete them.
You can also slice and dice using the Boolean operations under the Shape > Operations menu.
