Windows Update Repeats same 4 updates every time

When you see the updates, click on it and then hide.
You must set the windows update to notify and not to install automatically.
You will not be bothered again.
Windows Update Settings - Change

Three of the four updates are security patches, so you'll eventually want to get them installed.

Please attach the c:\windows\logs\CBS\Checksur.log

What are the optional updates?

1) Try booting into Safe mode and run SFC there. Post the new CBS log

2) Try installing one at a time (untick the others)

If the above work arounds don't help, see if any of the online MS fixits help.

I'll look at the CBS and Checksur logs if you want to wait on the MS fixits.

MS Fixits: Click the MS fixit that applies to your system.
Troubleshoot problems with installing updates - Windows Help
How do I reset Windows Update components?

I think that the OP is saying that they are installed, just keeps getting them again.
If I am mistaken, finding a way to install them would be the best way to go.

Please follow the Windows Update Posting Instructions and post the requested data
If the file is too large (8MB compressed), remove the older CBSPersist cab files until the final file is below the limit - you can always post them separately after zipping them. (the forum doesn't allow the upload of bare CAB files, for a number of reasons)
Also, please attach the C:\Windows\windowsupdate.log file to your reply.

You had a VERY large number of problems, according to CheckSUR...

Code:

Summary:
Seconds executed: 1337
 Found 22236 errors
 Fixed 22234 errors
  CSI Manifest Missing Total count: 1
  CSI Missing Component Key Total count: 3567
  Fixed: CSI Missing Component Key.  Total count: 3567
  CSI Missing Pinned Component Key Total count: 666
  Fixed: CSI Missing Pinned Component Key.  Total count: 666
  CSI Missing Identity Total count: 4236
  Fixed: CSI Missing Identity.  Total count: 4236
  CSI Corrupt Identity Total count: 2
  Fixed: CSI Corrupt Identity.  Total count: 1
  CSI Missing C Mark Total count: 4557
  Fixed: CSI Missing C Mark.  Total count: 4557
  CSI F Mark Missing Total count: 9873
  Fixed: CSI F Mark Missing.  Total count: 9873
Unavailable repair files:
 winsxs\manifests\x86_as`net_com`iler_b03f5f7f11t50a3a_6.1.7600.16385_no~e_ed4e6s0f14dce27e.manifest

The remaining problem indicates that the source of your problems may be hardware - probably RAM.

Please follow the instructions at RAM - Test with Memtest86+ and post the results.

OK - we'll try fixing the remaining errors...

I need to have a look at your COMPONENTS registry hive

Please copy the C:\Windows\System32\config\COMPONENTS file (no extension) to your desktop and then compress it - upload the compressed file to your favoured fileshare site (preferably Dropbox or OneDrive) and post a link.