Hi Juli,
I've never handled all three of the cameras you mention, but I would encourage you to do so. Go to a good camera store and handle each one to see what feels good to you. Nothing is worse than making a big investment and always saying -- jeez, I hate the fact that my wrist always hurts, etc. You can also compare viewfinders and actually try out the live view. I say the last thing because live view, as currently implemented in DSLRs, is not the panacea many think it to be. It is not nearly as "snappy" as compact cameras because the camera is actually moving a physical mirror to take the picture. In other words, shutter lag is an issue with live view. If you do a lot of manual or pre-focusing or if you plan to do a lot of studio shooting then live view has potential, but make sure you try it out and are comfortable with the timing.
With Nikon or Canon, you'll have a wider selection of lenses, because of the availability of third-party providers. The Olympus digital lens line is a bit more limited, but they do have a few very, very nice, low-f-stop telezooms that are, from all reliable reports, fabulous optics. Also keep in mind that the E-410, from the reviews, probably doesn't have the processing engine to live up the lenses. The E-3 is another story but much more money. They do have a new 70-300, but it not in their "professional" line (no weather sealing (not an issue with the E-410, because it isn't weather sealed either) and higher f-stops)). If you are not looking for "professional" quality, but still want decent photos, the E-410 plus the 70-300 might be the cheapest way to get a lot of reach.
For nature shooting, really look in to the value lenses offered by some manufacturers. I know some people who bought into Canon just to get a particular lens (candidates are usually the 70-200 f4 or the 400 f5.6, which are both really sweet lenses for the money). I know others (at the other end of the spectrum) who bought into Nikon because they fell in love with the 200-400VR. But if you're making decisions based on the availability of $4000 lenses, you can probably afford a bit more expensive body to match.
Not sure if any of this helps, but good luck anyway!
Mike