If you are working on the web, you can use Mapbox studio, leaflet.js or cartodb.com.
The main issue to start with is converting your data too a more web oriented format. You can probably export to .json from mapinfo (mapinfo plugin here http://communitydownloads.pbinsight.com/code-exchange/download/mapinfo2leaflet/ or online converter here http://converter.mygeodata.eu/). For xlsx, I'm assuming it is geographic data with x, y. If so, I would either bring into mapinfo to export as json or use a csv to json converter (http://www.convertcsv.com/csv-to-json.htm.).
The other thing to look out for is map projection. Convert your data to Web Mercator because that is what most web maps use. http://epsg.io/3857
If this seems complicated, I would just start by searching for leaflet or mapbox tutorials.
On desktop (MapInfo, QGIS, ArcGIS) you can download excerpts of OSM and import to overlay with your data.
Downloads can be found at various sites