Isn't it amazing how easy it is to overuse the word amazing? Prodigious is a more specific descriptor. Like amazing, prodigious conveys a sense of wonder, but it is used to comment on the size, amount, extent, or degree of what is being described. Items described as prodigious are extraordinary by one of these measures, as a musician with prodigious talent, a research grant of a prodigious amount, or a career notable for its prodigious output.
The adjective beautiful means "having beauty; delighting the senses," but on its own, it doesn't specify much beyond that. To call something exquisite, on the other hand, is to highlight a degree of rarity, and to suggest delicate or intricate qualities. The word exquisite comes from the Latin adjective exquīsītus meaning "meticulous, chosen with care." Indeed, items that are likely to be called exquisite, such as a fine wine, an impressive painting, a quality piece of furniture, or a piece of fine jewelry, are meticulously crafted.
When something is so bad you're shocked by it, atrocious may be the only adjective that fits the bill. In an exaggerated sense, atrocious can refer to something tasteless or unbearably bad. For example, "She was wearing an atrocious hat," or "His spelling was atrocious." In these examples, the offense is relatively minor. But atrocious can also be used to describe something of much greater offense marked by extreme cruelty.