"explain how the structures of the epithelium and muscularis of the small intestine, stomach and esophagus follow their function"

Stomach: Has three major layers - the mucosa, submucosa and muscularis externa.
1) The mucosa is formed by simple columnar epithelium that has the gastric glands and gastric pits, and the muscularis mucosa (it's muscle). When the muscularis mucosa contracts helps to expel the contents of the gastric glands. The cells in the epithelium secrete hydrochloric acid, mucus, pepsin ( breaks down proteins), and lipase (breaks down fats).

2)The muscularis externa layer is composed by  three(or two) layers of muscle, all with different directions. The contraction of all this muscle layers help to break up the food mechanically, forming the peristaltic movements. 

Small intestine:

3) The epithelium of the small intestinal is composed of simple columnar epithelium (most the cells are enterocytes). The epithelium forms microvilli that substantially increase the surface are for absorption of the nutrients passing. There are other cells, that produce mucus for lubrication of the chyle and to protect the epithelium.

4) Just like in the stomach, the muscularis externa layer is present in the small intestines as well and contains two layers of smooth muscle, an inner circular and outer longitudinal layer. They are important for peristaltic activity of the small intestine.

Esophagus:
5) Esophagus's epithelium is non-keratinized stratified squamous and the fact that is like this turns out to be more efficient at keeping out foreign antigens. The esophagus has to be protective,since it's close to the outside, plus needs to endure a variety of food and drinks (spicy hot, cold).

6) The muscularis externa of the esophagus has two layers, the inner circular and outer longitudinal layers of smooth muscle, with innervation between them. The first 1/3 of the esophagus has striated/ voluntary muscle, while the latter 2/3 is involuntary smooth muscle. All these muscles are necessary to move the food down to the stomach.