My startup disk is full and my iMessages are not coming in how do I fix this so that my imessage conversations on my iPhone can be seen on my mac

Disk is full?

Go step by step and check.

1. Start up in Safe Mode.

http://support.apple.com/kb/PH11212

2. Backup your computer.

3. Empty Trash.

http://support.apple.com/kb/PH13806

4. Disk space / Time Machine ?/ Local Snapshots

Local backups

http://support.apple.com/kb/ht4878

5. Delete old iOS Devices Backup.

iTunes > Preferences > Devices

Highlight the old Backups , press “Delete Backup” and then “OK”.

http://support.apple.com/kb/HT4946?viewlocale=en_US&locale=en_US

6. Re-index Macintosh HD.

This will take a while. Wait until it is finished.

System Preferences > Spotlight > Privacy

http://support.apple.com/kb/ht2409

7.Try OmniDiskSweeper. This will show the storage size details of the items.

https://www.omnigroup.com/more

Select Macintosh HD and click “Sweep Selected Drive” at the bottom.

Be careful. Delete only the files that can be safely deleted. If you are not sure about any file, don’t touch it.

8. Move iTunes, iPhoto and iMovie media folders to an external drive.

iTunes

http://support.apple.com/en-us/HT201562

iPhoto

http://support.apple.com/kb/PH2506

iMovie

http://support.apple.com/kb/ph2289