Most mead today is "spiced" mead, meaning it has some sort of fruit added in along with the honey to give it some flavor. I understand it's rather bland made with just honey.
River spirits are made from rope reed, and have an average value. Rope reeds grow next to water in the wild and their only other use is to make cloth, so they're probably literally just some tall fibrous reeds. They can be brewed so they must have a good deal of sugar in them, but since they're inedible it probably isn't any kind of sugar sentient creatures can use for anything. My guess is that river spirits are smooth and refreshing but very neutral in terms of taste.
Dwarven rum probably isn't meaningfully different from IRL rum. Sweet pods are a plant and not a mushroom (they have seeds instead of spawn) and can be made into sugar/syrup as well. You could probably tell the difference, but there's not really room to speculate on what that difference might be.
Whip wine is made from whip vines, and it's more valuable than the average drink but less so than sunshine. The vine can be milled into flour too, which is also more valuable than other grains. Whip vine could be a play on the shape of the plant (Urist likes them for their length) but I like to think that the name is also evocative of the flavor. It's got some bite, like a whip, so it's got a sort of peppery/spicy undertone to it that makes it much tastier than regular grains. Whip wine would probably be like a hoppy beer, then, but without the bitter aftertaste.