Switching to Leaflet is easier, and it accepts GeoJSON with FeatureCollection. You can also get attributes from a popup when you click objects.
However, Openlayers also have access to FeatureCollection. The mobile (jQuery Mobile) example for Openlayers demonstrated access to properties.
http://openlayers.org/dev/examples/mobile-jq.html#mappage
Click on the black icons and you will see a pop-up window with these attributes.
This is part of GeoJSON in the mobile example.
{ "type": "FeatureCollection", "features": [ { "type": "Feature", "geometry": {"type": "Point","coordinates": [1332700, 7906300]}, "properties": {"Name": "Igor Tihonov","Country":"Sweden", "City":"Gothenburg"} }, { "type": "Feature", "geometry": {"type": "Point","coordinates": [790300, 6573900]}, "properties": {"Name": "Marc Jansen","Country":"Germany", "City":"Bonn"} }, { "type": "Feature", "geometry": {"type": "Point","coordinates": [568600, 6817300]}, "properties": {"Name": "Bart van den Eijnden","Country":"Netherlands", "City":"Utrecht"} }, { "type": "Feature", "geometry": {"type": "Point","coordinates": [-7909900, 5215100]} } ] }
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