Blending Modes and layer transparency are features most commonly associated with Photoshop and its Layers palette; it's the mission control centre when it comes to blending layers in Photoshop. You can achieve the same result in Illustrator, but rather than blending pixels, you're blending shapes. And here, rather than controlling it all from one palette, you must learn to use three different palettes together.
The Appearance palette, the Transparency palette, and the Layers palette all work together when it comes to blending shapes, groups, and layers within Illustrator. With the Layers palette you can specify your target - it can be a single object, a group of objects, or an entire layer. The Transparency palette is the place where you can alter the Blending Mode and opacity of your object. The Appearance palette enables you to target the stroke or fill of a shape independently, altering either the stroke or fill while leaving the other untouched.
Once you get into the routine of using the three palettes, the flexibility of using them becomes quite evident. And it won't be long until it feels intuitive.