my nephew's one year old drinks and eats very little, what could be the problem? He seems hungry, and tries to eat, but he would keep it in his mouth for a long while then spits it out. We give him mashed potato, yogurt and baby food, but he would only eat the most 3 teaspoonfuls, then refuses to eat more. He is a year old and he is only 16 pounds.
First off, your nephew's parents need to be discussing this with their pediatrician. Your nephew's weight is extremely low for his age; 16 pounds would be below the first percentile. 18.5 pounds is the 3rd percentile for that age according to the CDC growth charts. There may be particulars affecting this child (was he premature?), but regardless, this should be primarily a call to the pediatrician. He may also have some persistent medical issue, such as GERD/acid reflux, that makes it hard for him to eat, or an enlarged thyroid or other issue in his throat making it hard to swallow, or any number of other issues.
For the general case of your question - what do I do about a child who doesn't eat - there are a lot of potential solutions.
First thing I'd address is texture. The child may be unhappy with the textures he's being provided. My first son was a huge fan of cereals and blended vegetables, and ate 'baby cereal' from 4 months to 8 months happily, then transitioning to more solid foods at that point. My second son hated cereal or blended vegetables, and was eating finger foods at five months exclusively (plus breast milk of course). All of the foods I see above are soft texture; perhaps this child prefers crunchier or tougher textures.
Second thing I'd address is taste. Some children like stronger tasting foods, some blander tasting foods. Try making your own food, rather than baby food in jars; Gerber-type foods don't really taste very good. Steam the vegetables and then use a food processor if needed (though by one, he's probably fine with steamed vegetables). Hamburger is excellent for that age also as it's easily eatable as a finger food. Fish is also good - poach it in broth, steam it, grill it, or bake it, depending on the fish, either way it'll be nice and flaky and easily eaten as finger food.
Finally, consider feeding more often small meals. Three spoonfuls every hour would get enough food in him. Work his way up, don't stress too much about quantity and he won't be to stressed out.