Hi Ian. My ears were burning so I thought I would post a reply to your question. I have no experience of the E-620 but, as Steve said, I have an E-30 and also an E-510. From the reviews I have read it appears that the E-620 and E-30 are broadly similar but with different body sizes and a few more features on the E-30. The IQ from both is meant to be pretty much the same and the E-620 has a slightly higher spec LCD.
Your reasons for looking at the Olympus range echo my own. I wanted a light, compact system which I can carry easily when I am walking about. I am not interested in sitting in a hide all day with a big lens on a tripod. The in-body stabilization works well and all my shots are taken hand held. How successful they are is a matter of opinion but you can see them in my Gallery. Last week I ordered the 50-200 lens, which is faster and slightly sharper than the 70-300. However, when I tried it on my camera it was much heavier than my existing lens and I found that my arms were beginning to ache after a little while playing with it indoors. I decided that it didn't really suit my requirements, so I returned it for a refund. The 50-200 is lighter than the Canon and Nikon 400 lenses which are commonly used so I can empathize with your experience with them.
The E-620 and 70-300 lens is an excellent combination for the money (even better for the next two weeks with a cash back on the lens from Olympus). It is capable of very good results with a bit of care and under the correct conditions. I use the EC-14 teleconverter in the summer, when the light is better (it reduces the aperture by one stop). It degrades the image very little but it is essential to avoid movement at that focal length. As with any system, though, there is no substitute for getting close to the bird for best results. As Steve says, Olympus is not the ideal choice if there is any prospect in the future that you will want a longer lens. In your case that doesn't sound likely, so I would suggest trying them out if you can find somewhere with them in stock. They really are very good.
Finally, I know 'Amadoux' recently purchased an E-620, so it is possible you might get a post from her to give her opinion.
I hope this helps a bit.
Ron