Bulk Deleting Old Emails from Outlook
To bulk delete old emails or find attachments you can use the 'Mailbox Cleanup' tool located under File > Tools

A Useful Button
Before we begin, there's a useful button at the top of the 'Mailbox Cleanup' window called 'view mailbox size'.
Here you can view your local, and server-side mailbox sizes.
As everything stored locally is downloaded from the server, just focus on the 'Server Data' tab if you want a better idea of where your data is being stored. Divide the numbers by 1000 to make things more readable i.e. 821768 KB = 821.8 MB (rounded up)

You also have a list of every folder you've created and their size. This can help you quickly identify which folders are storing the most data.
NOTE: As described in the screenshots above, 'Size' is the folder size without subfolders, whilst 'Total Size' is the folder size including subfolders.
Standard Outlook folders to look out for are 'Sent Items' and 'Deleted Items', they often contain a lot of data and can build up quickly.
Find and Delete
Pressing 'Close' on the 'View Mailbox Size' window will take you back to 'Mailbox Cleanup'
Here you can search for emails older than a certain number of days, or emails larger than a certain amount of kilobytes.

NOTE: When searching for items of a certain size, 1 megabyte = 1024 kilobytes
Regardless of your choice, it'll open a box like this.

Here you can define specific parameters to ensure Outlook searches for the specific emails you want.
A useful option to search for emails that weren't sent to you directly is 'Where I am on the CC line with other people'.

As the name suggests, this will pick out emails where you don't appear on the 'To' line, but you do appear on the 'CC' line.
This may contain company wide or informational emails which are no-longer relevant.
Another useful option under the 'More Choices' tab is 'Only items with one or more attachments'.

95% of your mailbox is likely to be attachments, so it makes sense to store them elsewhere if they're important.
NOTE: Attachments can include images that get sent over in your signatures, if you receive a lot of emails, these unnecessary images can add up.
Once you've dialled in your search parameters, you can click 'Find Now' in the top right, and after a little while, emails will populate at the bottom of the box.
You can select and delete emails as you see fit, these will end up in your 'Deleted Items' folder, please remember to clear this out regularly. Your deleted items folder isn't somewhere to store important information.
Double-clicking any item will open it up should you need to know more about it before making a decision.