Tim, Ohio:
The tools that work best depend quite a bit on the size of the work you are doing and the material you are working on. What works on horn does not always work on elephant ivory or bone or whale ivory. The following is obviously on whale ivory. The tooth is about 4 inches tall. The image is fairly large and whale ivory doesn't have anywhere near as much "grain" to it as horn does and it has none of the porosity of bone. A scribe, like a sharpened sail makers needle works well for most of the lines. I did this tooth at sea 30 years ago and the only tool used was the sail makers needle.
The next one is an engraving on elephant ivory and the ivory plaque is about 1 3/8" x 2 1/2". The elephant ivory is softer than the whale ivory and responds well to a knife graver, scribe, and tiny knife point. You can use larger tools on a piece like this because the image is so large. This engraving is also 30 years old.
The next image is done on horn - it is very soft, very grainy and the consistency of the horn material can change drastically all over its surface. Some places it is really hard and flinty, others it will be gummy, and still others it will chip and flake. I often change the type of tool I am using as the characteristics of the horn change in different areas of the design.
The next photo shows several items of gold jewelry that I made for my wife and daughters. The largest pendant is only about 3/4" top to bottom. These are whale and elephant ivory. The images are very small (the ivory part of the earings is only 1/4" top to bottom) so the tools need to be very small as well.
The tools I use, mostly, are shown below. From left to right they are, a small square graver (for heavy lines), a knife graver (for thinner lines), a carving knife for larger images or longer straight lines, a carbide scribe / burnisher for finer lines and to help correct errors, a replaceable point scribe into whick I place dental burs of various types (very handy), an oral surgery scalpel for very small knife work, a sail makers needle, and a surgical scalpel with replaceable blades for fine shading.