I am fairly sure you can do this with what you have. With the layers that you have clipped I think you can right click on the layers and go down to Data, then select export data, and export all features in view extent, also when you do that make sure you have zoomed out to see the whole layer you are trying to export.
If that doesnt work then do what the previous reply said and use the Clip Tool. If you are unsure of setting up the feature class all you need to do is either create a new file geodatabase in your catalog window or use your default geodatabase, then right click on the geodatabase and select new feature class, Give it a name, and make sure you have Polygon Features selected as the type, then on the next page select your coordinate system you are using. Then unless you know your specific needs i would leave the rest of the tabs at the default. Once the feature class is created, go to the editor tool bar and select start editing and select the feature class you just made, then go to the far end of the editing tool bar and select create feature and draw your polygon, when you have drawn it, select save edits on the editing tool bar, then select stop editing and then you can use your polygon to clip the features!
Hope that helps!
