I'd list the company, list all three titles, most recent on top, oldest on the bottom, put in parentheses "titles differ due to being in different departments, significant overlap in duties," then list your job duties there treating it as a general bucket for all three. If anyone is flummoxed by that setup, they'll ask you about it in your interview or phone screen.
Include the duties, but if you're interviewing for a job that wants specific technical skills, a laundry list of all tasks you do won't interest them. Stick to relevant ones (will also be taken as an indication that you are paying attention to the job posting and how you might fit).
Also, again, you don't just want to list what you did. Companies are very interested in what you've accomplished for your employers. If you made your job better or made the company better, make sure you list that. It's much more important.
"In charge of widget inventory system"?
or "Took charge of widget inventory system and improved delivery time by 18% and reduced inventory order backlog by 45%."
The second is a much more strategic view of what you've done with a demonstrated impact and added value to the company bottom line. If it's more service oriented, then service delivery metrics can be used.