You can create Graphic Styles within Illustrator by using the Graphic Styles Panel (
Window > Graphic Styles). The purpose of Graphic Styles is to quickly apply the same appearance to multiple objects or to create a library of commonly used appearance settings. In function, they are similar to the "Styles" panel within Photoshop (but not the actual Layer style options).
Simply create an object with the appearance you want, then drag that object to the Graphic Styles Panel.
When you want to apply the same appearance to a new object, select the object and then click the style in the Graphic Styles Panel to apply the style to the object.
To change or update a Graphic Style, start with an object set to the style, alter it how you'd like. Then drag the altered object to the Graphic Styles Panel while holding down the Option/alt key and hover over the existing style. When you see a dark black outline in the panel, let go of the mouse. The style will be updated and all objects with that style applied will update as well.
If you need to reuse styles you've created for other projects, it is possible to save them as an external (.ai) files, and in turn reload them any time, from the menu for the Graphic Styles Panel. There are also several Adobe installed styles available in the
Open Graphic Style Library menu item.
You can read more about graphic styles in Illustrator at Adobe's site.