I recently had to import some of my old emails I have in PST format to my Outlook and Gmail and this is how I did it.
What you need
Thunderbird or any mail client that suppot IMAP
Gmail account with IMAP enabled - go to gmail > settings > forwarding / POP IMAP click enable
Outlook version of your PST file
An internet connection
Step 1 - Setup Thunderbird to get mail and connect to your Gmail using IMAP - instructions here
Step 2 - Import the PST file to your Outlook
Step 3 - Go to Thunderbird and import mail from Outlook
Step 4 - You should now see your PST mails in your Thunderbird by now, you should have 2 Main folders one from your Outlook PST mail and one Gmail folder, all you have to do is drag and drop the mails folder you want to your Gmail folder in Thunderbird or copy and paste it then your Done.