For the record, as mentioned elsewhere in the thread obsidian is a kind of naturally occurring glass. The obsidian short swords in the game most likely resemble a macuahuitl, which was more akin to a bladed club studded with pieces of razor-sharp obsidian than a whole blade made out of glass. (Which would be stupid and probably break within a few swings.) In any case, tools and weapons made with glass edges should wear down quickly, but be terribly lethal while they're intact.
Obsidian is used in scalpel blades today for the same reason it made fantastic arrowheads and tools thousands of years ago. While our ancestors didn't know it, glass - obsidian being a popular and naturally occurring variety thereof - is an brittle amorphous solid. This means that the material isn't limited by its own crystalline structure, and can be worn or compressed down into shapes that would be impossibly thin for other materials. The way it naturally fractures produces these incredibly thin, incredibly sharp edges, making obsidian and other glasses ideal for making pointy objects of the finest quality with relatively little effort. When it comes to being sharp, objects made from glass will have that in spades.
The problem is that glass is brittle, and tougher glass-like materials like bulletproof glass require special treatment processes and substances that wouldn't appear in Dwarf Fortress. This limits the usefulness of glass in objects like armor, where in most cases they'd be worse than useless. Arrowheads and bolts could be made with glass and would be remarkably lethal if only because they're so sharp. (Not just because they could shatter, but because they'd slice through flesh like a hot knife through cold butter.) Low-durability knives and the club-like obsidian short swords should be options as well, in addition to glass-headed spears, but the key there is durability. They'd be amazing for a few strikes, more if you're careful or if the target lacks armor, but quickly lose their finish and require replacement after striking something hard a few times too many.
Oh, and as for the clay bit, now that kaolinite is in the game, making porcelain is definitely possible. I say go for it.