Yes you can force-dry smaller pieces of wood successfully at home and a toaster oven is a good way to try it out. You can of course also use a conventional oven in the same way. But in either case it is not advisable to again use the oven to cook in as heating the wood will release extractives which can turn into noxious and/or harmful compounds at the higher temperatures used for cooking. At the very least it can impart "off flavours" to foods.
Low temperatures for a long time is the way to go with conventional heating and depending on how green the wood is to begin with and how dry you want it to end up you may be looking at baking the wood for more than 24 hours.
Because wood varies so much obviously results can be very varied, which is why there are as many reported successes as failures if you read up about attempts to do this. But another reason is that the thermostats on ovens (even full-sized ones from well-respected brands) are often very inaccurate — reportedly as much as 50° off the stated temperature — so as with temperature-sensitive cooking tasks it is advisable to rely on an in-oven thermometer to accurately gauge the internal temperature.
In addition to the thermostat inaccuracies ovens don't maintain temperature very well and I believe toaster ovens are particularly noted for this. So if you want to maintain a more consistent temperature one method is to use a large 'heat sink' within the oven, which can be nothing more sophisticated than a shallow pan full of sand. A large piece of cast iron cookware would do a similar job.
Alternate method: microwave
Another option to speed drying of wood is to use a microwave. I heard about this first used by turners who were seeking to speed the process up when starting with green wood. I've used microwaving myself with great success. My own experiments have confirmed in a very unscientific way the accepted practice here: short blast, long wait, short blast etc. Approximate times for single pieces were 10-20 seconds, wait for 2 minutes or longer, repeat.
What you're seeking to do is keep the temperature fairly low; you don't want to boil the water in the wood as this can weaken the structure and in addition it produces "wood steam", which can smell unpleasant and can linker for weeks. Or months.