Intestinal Obstruction: The symptoms of abdominal pain relieved by greenish vomit, no passage of stool or flatus since onset, and the absence of guarding or abdominal swelling are highly suggestive of an intestinal obstruction. The greenish vomit indicates that the obstruction is likely in the small intestine, as bile is present in the vomit.

Gastroenteritis: Although less likely given the specific symptom of no passage of stool or flatus, severe gastroenteritis could potentially cause these symptoms, especially if there's a significant ileus component.
Appendicitis with Early Obstruction: In some cases, appendicitis can cause enough inflammation to obstruct the intestine, leading to these symptoms. However, the absence of guarding and the specific nature of the pain and vomiting might make this less likely.

Volvolus: A volvulus, which is a twisting of a portion of the intestine, can cause an obstruction and severe symptoms. It's less common but critical to diagnose early due to the risk of ischemia and necrosis of the bowel.
Mesenteric Ischemia: This condition, involving insufficient blood flow to the intestine, can present with severe abdominal pain out of proportion to the physical examination findings. The vomiting could be a late sign, and the absence of bowel movements could indicate ischemic bowel.
Perforated Visrus: Although the absence of guarding and abdominal swelling makes this less likely, a perforated viscus (such as a perforated ulcer) can sometimes present atypically, especially in early stages or in patients with significant comorbidities.

Intussusception: More common in children but can occur in adults, intussusception is a condition where a part of the intestine telescopes into another part, causing obstruction. It's rare in adults without a lead point like a tumor.
Internal Hernia: An internal hernia, where intestine herniates through a defect within the peritoneal cavity, can cause obstruction. This is less common and might not always present with typical signs of obstruction.