Having some experience in the medical feild, It all depends on a variety of things...have they ever pooped like this before? Do either of them have a fever? Is their stool firm? Or is their stool very loose (diahrrea)? How long has this been going on? Do either of them have abdominal tenderness? For your 16 month old-did you introduce formula or cow milk into the diet? Any nasuea or vomiting in either of them? Are they irritable, extremely fussy and clingy?
Another thought... most bugs that affect the stomach are viruses. Which basically means their is no medicine that your kids could take to make the bug go away-so you would just have to wait it out. If they are both expereiencing diahrrea the most important thing you can do is to make sure they stay hydrated. You can have them drink pedialyte. besides fluids, pedialyte has electrolytes (mostly Sodium and Potassium) that are essential for our health.
One note on your son with the dark balck poop. If you notice he becomes dizzy, or passes out I suggest taking him to your nearest ER. Really dark poop (black and tarry looking) is indicative of an ulcer in the upper GI. By the time the red blood goes through the entire GI tract it gets processed and turns black. If your son has been on NSAIDS such as tylenol, and Ibuprofen for a long long time (like months to a year-everyday-continually) he is at risk for stomach ulcers.
My main advice is if YOU DO NOT FEEL LIKE THEY ARE IN IMMEDIATE DANGER, I wouldn't take them to the doctor. There is no point in wasting insurance and a co-pay on someone to tell you that your kids are okay, or that there is nothing he can do because it is a stomach virus.
Sorry this was so long! I hope it helps. Good luck with the weird looking poop!