First, I am glad to hear that it isn't black since that would raise worries of gut bleeding. In any case, given that Ozzy's signs came after eating grease, we'd be most wary that we have a severe gastroenteritis or pancreatitis present.
With this all in mind, as long as he can keep a bit of water down, we can try some home supportive care to try to settle his stomach. To start, if he hasn’t just vomited (since otherwise we’d need to rest the stomach for a few hours first), you can consider treating with an OTC pet safe antacid [ie Pepcid (More Info/Dose @http://www.petplace.com/article/drug-library/library/over-the-counter/famotidine-pepcid), Zantac (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/ranitidine-hcl-zantac), Tagamet (More Info/Dose Here @ http://www.petplace.com/article/drug-library/library/over-the-counter/cimetidine-hcl-tagamet)]. Whichever you choose, we’d give this 20 minutes before offering food to allow absorption. Of course, do double check with your vet if he has a known health issues or is on any medications you haven't mentioned. Also if you give this and he cannot keep it down due to nausea that is usually a red flag that we need to bypass his mouth with injectable anti-vomiting medication from his vet.
Once he is more settled, you can plan to try small meals of a light/easily digestible diet. Examples you can use are cooked white rice with boiled chicken, boiled white fish, or scrambled eggs, or meat baby food (garlic/onion free only) There are also OTC vet diets (ie Hill’s I/D or Royal Canin’s sensitivity) that can be used too. The aim of these diets is that they will be better tolerated/absorbed by the compromised gut. Therefore, it should get more nutrients in and result in less GI upset. As long as improvement is being seen, I usually advise continuing this until the signs are settled, and then weaning slowly back to what you normally feed.
Since dehydration is a risk here, we need to keep an eye on his hydration. To check this and make sure dehydration isn’t an issue, there are a few parameters you can test. Further to checking for gum moisture, you will want to make sure his eyes are not looking sunken and that he doesn’t have a "skin tent" when you lift the skin. To see how to check these, you can find a good video HERE (http://www.ehow.com/video_12232503_dog-dehydrated.html). If you do see any of these signs already, then that would be our cue to have him seen before this becomes an additional issue (especially since its often dehydration that makes them feel unwell).
Finally, as long as there is no blood in those stools, you can consider trying a pet safe anti-diarrheal. As I am sure you appreciate, these would not be a cure for infectious issues; but it can still be of benefit. It will reduce diarrhea load, allow the body to absorb more water/nutrients, and soothe the upset gut. In regards ***** ***** options, the one we most commonly use is OTC Kaolin/Kaopectate (More Info/Dose @ http://www.petplace.com/article/drug-library/library/over-the-counter/kaolin-and-pectin-kapectolin-k-p)). Otherwise, Propectalin, Canikur, Fast Balance, and Protexin Pro-Fiber (which is available OTC at vets, pet stores, and even Amazon) would be another option. All will slow diarrhea and those last ones have the added bonus of providing support to the delicate good GI bacteria. So, these can be used as a short-term means of soothing his upset GI.
Overall, I do suspect that the grease has given poor Ozzy a pancreatitis or gastroenteritis. At the moment, the above would be our point of call but if he cannot keep that or water down, appears dehydrated already, or doesn’t respond to the above within 12-24 hours; then we'd want to get his vet involved. They can assess his hydration, rule out fever, ensure nothing in his stomach that shouldn't be, or any sinister viruses present. Depending on their findings, his vet can treat with injectable anti-vomiting medication, fluids, +/- antibiotics to settle this for him.
Please take care,
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