"My current strategy is to target the top 3 all on one page."
Definitely have one page for all those keywords. "Managed IT Services" and "IT Managed Services" are the same thing. Even "Managed IT Support" could be considered the same thing. Google's algorithm is smart enough to decipher synonyms.
Resource: http://helpmyseo.com/seo-tips/296-language-synonyms-and-the-google-algorithm-and-how-it-affects-your-seo.html
"The problem then is the title tag: Managed IT Services | IT Managed Services | Managed IT Support"
Definitely do NOT do this. Google will see it as keyword spam/stuffing and it will hurt you, not help you. I'd recommend making the title tag "Your Company Name | One of those keyword phrases" (assuming your company name doesn't already have those phrases in the name)
Resource: http://www.pagetraffic.com/guide/keyword-repetition.php
"I could build pages for all 3, but how would I incorporate them into the website since they are all synonyms. . . How would handle separate pages with synonymous content?"
The way to handle pages with to avoid them like the plague.
Resource: http://moz.com/blog/duplicate-content-in-a-post-panda-world