Start with the right checks.
The warning may refer to mailbox storage or Microsoft cloud storage. Read its exact wording so you address the correct limit.
What to do next.
Open Outlook.com’s Settings and review Account, Storage and the relevant storage notice.
Identify which folders and attachments use space.
Preserve needed records in an approved location before removing items.
Review Deleted Items before emptying it, because those messages can still use mailbox space.
Check the result.
Recheck the quota and test sending and receiving with harmless mail. Ask for a resend if a message was rejected while storage was full.
Stop and get help if…
The account remains blocked, totals do not make sense or records must be retained for work. Review the account and retention requirements before a bulk cleanup.