You can add more than one selector to a text animator. Selector 1 can control the slide in, twirl down the Animator>Range selector>Advanced properties and look for the control called Based On, and set that to character.
To have a slide-on you would add an offset to the position, and then change the selector so that it progressively de-selects the text. The best way is to set the start and end to 0% and 100% respectively, and the add keyframes to the offset property, starting at 0 and ramping down to -100%.
Now hit the Add button next to the Animator and choose Selector>Range to add another selector to it. Make sure that it is selecting none of the text to start with. Change the Based On property of this selector to words. You can change the way the two selectors interact with the Mode control, this changes whether the selection properties add together, intersect, subtract and so on. Using the **Add* mode should work for you. With this selector you would keyframe it so that it progressively selects the words in the text when you want it to slide out. Use the same technique as the first selector, but with the keyframes reversed.
This will make the slide go back to where it came from, you might want it to continue in the same direction. To do this you would add another animator with a different offset, rather than just a selector. You can add as many independant animators to a text layer as you like.