you just need to backup the file outlook.pst do a search for it, but its generally in your office folder.
OST files mean that your outlook is using microsoft exchange... PST files are when you download the mail locally. if you are using exchange then the backups should be done by your server admin, not you. The OST files ONLY KEEP LOCAL DATA - this can be configured to include your email, but by default does not.
356mb isnt that big mate, my PST is over 2gb in size, but it all depends on what you are receiving and how much of the other outlook features you use, ie, calendars contacts, tasks etc. etc.
You need to Convert Outlook OST files to Outlook PST, Emails and Messages. these new files capable every require action for Emails clients. see : ostfile.co.uk
If file is opening with ms outlook whether it is ost or pst, you can backup it using below given steps: Open ms outlook Go File > Import & Export > Export to a file > Personal storage file Select the mailboxes which one you want to backup (by default all) Proceed for next and set a location where you want to save exported i.e. backed up data Finally click on export, all mailboxes will backup in .pst format. Note - Ost file can not be open with any other environments or applications. PST file can be open with ms outlook anywhere so must keep the backup in pst format.
Without converting OST file data into PST file format you can't access your Outlook emails files and folder I would like to suggest you use Kernel for OST to PST converter tool, this is an advanced tool to recover OST file from MS Outlook mailbox and convert OST to PST file format. for more info visit here:- http://www.osttopsttool.com and download free trial version of this tool from here:- http://www.ostpst.org