What version of Outlook and Exchange?
At a high level, do you need to use PST mode?
What type of account are you using? POP? IMAP? Exchange? If the latter
(via VPN or HTTP), then make your delivery location the Exchange mailbox, not the PST...then cached mode keeps a local copy. If POP, then configure the account to leave copies of messages on the server.
Just so you understand, in order for others to invite you to meetings, they need to get to the database on the server. Your local PST needs to synchronize and keep current with your calendar that is on the server.
The problem is that your local (pst) calendar is not in-sync with the server calendar. When other users invite you to a meeting, the request does not goto your PC, it goes to the server.