To hit the ball out of the park, swing with as much power as possible. Time your swing just right and you send it flying out of the park.
When batting, go in an upgrade as you hit the ball (up a few degrees when the ball is hit). This increases your chance of getting a home run.
In the Home Run Derby, it‘s all about timing. Don’t swing your entire hand. Instead, just flick you wrist quickly. Try swinging up on the ball instead of using just a straight swing. Make a quick "U" in the air with the Wiimote and keep the Wiimote parallel to the screen when you are done with your swing.
To get some easy homeruns, hold the Wiimote like a baseball bat but hit it like a golf ball instead. Make sure you swing hard. This will require practice.
When hitting the ball, hold LEFT to increase your chance of getting it out of the park, especially in Homerun Derby.