Gastroenteritis: This is the most likely diagnosis given the combination of epigastric pain, vomiting, and diarrhea. Gastroenteritis, often caused by viral or bacterial infections, leads to inflammation of the stomach and intestines, which matches the symptoms described.

Peptic Ulcer Disease: Epigastric pain is a hallmark of peptic ulcer disease, which can be exacerbated by vomiting, potentially leading to further complications like perforation or bleeding.
Gastroesophageal Reflux Disease (GERD): While more commonly associated with heartburn, severe GERD can cause epigastric pain and may lead to vomiting.
Food Poisoning: Similar to gastroenteritis, food poisoning from consuming contaminated food can cause sudden onset of vomiting, diarrhea, and epigastric pain.

Appendicitis: Although the pain typically starts near the navel and then moves to the lower right abdomen, some cases can present with epigastric pain, especially if the appendix is located higher than usual. Missing appendicitis can lead to rupture and severe complications.
Pancreatitis: Acute pancreatitis can cause severe epigastric pain radiating to the back, nausea, vomiting, and can be associated with diarrhea. It's a serious condition that requires prompt medical attention.
Intestinal Obstruction: This condition can cause severe abdominal pain, vomiting, and changes in bowel habits. It's a medical emergency that requires immediate intervention to prevent tissue death and perforation.
Myocardial Infarction: In some cases, a heart attack can present with epigastric discomfort or pain that may be mistaken for a gastrointestinal issue. It's crucial to consider cardiac causes, especially in patients with risk factors.

Inflammatory Bowel Disease (IBD): Conditions like Crohn's disease and ulcerative colitis can cause chronic diarrhea, abdominal pain, and sometimes vomiting. While not as common as other causes, they should be considered, especially if symptoms persist or recur.
Zollinger-Ellison Syndrome: A rare disorder characterized by excessive gastric acid production leading to severe peptic ulcers, diarrhea, and abdominal pain.
Eosinophilic Gastroenteritis: A rare condition involving eosinophilic infiltration of the gastrointestinal tract, which can cause abdominal pain, vomiting, and diarrhea, among other symptoms.