Birch wood is fairly well-known in some parts of the US as both a firewood and a smoking wood, though it may not be as easy to find as other more common smoke woods like hickory or mesquite. Because it is a hardwood, birch gives off a clean smoke. In comparison, resinous softwoods like pine put out a sootier smoke that can cause creosote buildup on foods. The residue from softwood smoke gives food an unpleasant taste and can contain carcinogens. Note that birch is considered by some to be a softwood and has a particularly oily bark that gives off a black smoke when burned; however, the oiliness is concentrated in the bark and the rest of the wood is in the medium-hard category. This means that it is softer than some other hardwoods, but is still in the hardwood category. In other words, it should still be safe to use for smoking food.
Orange wood is not exactly the most widely known smoking wood. This is largely because orange trees are not very common outside of a few states. As with the wood from all fruit trees, orange wood is a hardwood. Because they are made from a hardwood, orange wood chips put out a cleaner smoke than softwoods. It does not have the resinous nature of pine and fir, which can leave an unhealthy residue on food.
In the US, beech wood is better known as a firewood than as a wood for smoking food. This is especially the case with the parts of the country where barbecue is a major part of the culture; however, it can be used to provide flavor to meats and other foods. Beech is a hardwood, which means that it will not put out the high levels of thick smoke that you would get from a softwood like pine or fir. Along with the potential for acrid-tasting creosote buildup on your food, the smoke from softwoods is filled with potentially harmful compounds. In comparison, beech wood chips will give you a light blue smoke that provides a flavor that is mild and sweet. Along with its flavor, it will give lighter colored foods an attractive golden color.
Like all the various forms of barbecue, jerk relies on smoke for flavoring. In Jamaican jerk, pimento wood is the source of the smoke and the flavor. The flavor that pimento wood provides is one of the distinctive qualities of the jerk style of cooking. While the traditional form of jerk involves the use of wood along with sticks and leaves, using chips can still provide a distinctive pimento taste that will set your food apart from food smoked with other woods.
Like all fruit trees, peach wood falls into the hardwood category. Hardwoods are recommended for use as firewood and as smoking wood, simply because they do not have the resins found in pine and other softwoods. The smoke produced by those resins negatively affects flavor and can pose health hazards due to the carcinogens it contains. In contrast, seasoned hardwoods like the wood used to make peach wood chips will burn clean with no residue. That smoke is light and pale blue, not thick and sooty like the smoke from some softwoods.