Hi Gene,
To get your labels to display in a SharePoint WebPart, ensure that you are adding an entire map service to the Web Part.
You can publish a map service with labels by either selecting Label Features in the Table of Contents in ArcMap, or creating an annotation layer before publishing your service. After the Service is published, add the entire map service to your Web Part from the Browse Panel, instead of adding the layers individually. Your labels should appear.
Annotation layers added individually are not currently supported layer types in ArcGIS for SharePoint.
Kelly