I'm limited to having either iron, tungsten, titanium, and gold be alloyed and/or made into a composite material with obsidian to make an obsidian-like material with a gold sheen that can be shaped under heat like a metal to be made into armor. I'm curious if it's believable enough or even possible, period.
Obsidian is basically glass with some impurities that make it absorb light. Like glass, it is very brittle, and makes terrible, very heavy armor. It can take a razor sharp edge, so is useful for weapons, if you don't mind the edge on your weapon snapping off anytime you hit anything harder than flesh.
What I think you want, rather than actual obsidian, is a metallic glass. This is a substance made of a number of different metals melted together, and then cooled so rapidly that the metal has no time to form a crystalline structure. This results in a very hard, durable substance that shares properties of both metal and glass. Vitreloy has a tensile strength double that of titanium, and there are tungsten alloys that have hardness double that of carbon steel. When heated, many metallic glasses will become extremely malleable, and can be easily molded like hot plastic.
The field of metallic glass is still very new, and experiments finding new alloys are being done every day. It's not unrealistic to think that one might be found that has a glassy black look with a hint of gold. The color of alloys sometimes has nothing to with their components. For instance gold-aluminum alloy in the right proportions will be a vibrant purple. Gold infused glass is called cranberry glass for its bright red color, and titanium infused glass is yellow.
As we enter the glass age, top labs such as Corning are beginning to develop glasses that have flexibility of plastics and the durability of metals. Since obsidian is glass with impurities, the first challenge would be to purify the glass so you had a good starting point. The second challenge is to infuse the right impurities to give the glad the potential for the kind of toughness you need, which will be a feature of how the ions are suspended in the Silicon matrix, not the starting material. The third challenge will be to establish the right heating and cooling cycles for tempering the glass to the right kind of toughness. The fourth challenge is to do that with the awkward 3D shapes of armor, arms, and implements.
Overall, it's a little beyond today's technology, but very remotely plausible with a little handwavium, to someone who has exactly the right kind of eclectic interests