In fact you add style to the vector layer, in which the features are stored, in your case it is named mapObject (but should be something like featureLayer or myVectorLayer or so). Here you can find a blog about stylig the vector layer and OpenLayers.StyleMap would surely be useful in this case.
If you need more styles (you have many different features to distinguish), you can also change the style of individual features based on "rules" (OpenLayers.Rule) and with the help of OpenLayers.Filter.Comparison you can assign different symbolizers to your features. A shord example of the styling:
myOpenLayersStyles.commentLayer = new OpenLayers.StyleMap({ //creates style for the vectorLayer features
"default": new OpenLayers.Style({
pointRadius: 20,
fillColor: "#0000ff",
fillOpacity: 1,
strokeColor: "#0000ff",
strokeWidth: 3,
strokeOpacity: .7,
cursor: "pointer",
cursor: "hand"
},{
rules: [
new OpenLayers.Rule({
filter: new OpenLayers.Filter.Comparison({
type: OpenLayers.Filter.Comparison.EQUAL_TO,
property: "completed",
value: 1
}),
symbolizer: {
graphicHeight: 25,
externalGraphic: "Img/comment_completed.png"
}
}),
new OpenLayers.Rule({
filter: new OpenLayers.Filter.Comparison({
type: OpenLayers.Filter.Comparison.EQUAL_TO,
property: "completed",
value: 0
}),
symbolizer: {
externalGraphic: "Img/comment.png",
graphicHeight: 25
}
})
]
}
)
});