“Which is better, park domain names externally or on our own landing pages?”
I've mentioned useful external parking tools like Sedo and Parked. Both excellent services and can help you benefit from domain name parking.
“Why park domain names? What do I get out of it?”
While there is a whole business of domain speculation, as a business-to-business firm with real solutions to sell, I want you to stay away from just randomly parking domain names.
“Are you familiar with SEDO? What are your thoughts about using them for our parked domains?”
Sedo is a great solution, I use it for buying domains. However, don't recommend them for parking.