Hello! Good-evening folks. I don't post on facebook. But due to to fact that this issue of privacy is not taken too serious by the higher-up I feel the need to educate the ignorant. I have seen some many post on facebook from my so called "facebook" friends" and trust me, not all are gratifying. 
Ok, here is the deal: not that I blame you, but it's still your handiwork indirectly. Remember those times when facebook was still the bomb, then you gave permission to any application that requires your facebook login? Yes, am sure you remember, also don't forget those games that you gave facebook authorization to post an update, view your friend list and use your personal data. 
To cut the story short, some of these "authorised applications" are responsible for posting those explicit and obscene stuffs on your wall. I find it really funny when I seen people saying their account was hacked; hacked by who,when, how and why? It has been hacked from the onset!
Solution: unsubcribe from those pages, de-authorise those applications. 
1. If you are using opera-mini for mobile phones like me then follow these step. >log in to your wall>go to "settings and privacy">under this go to "apps" it's has this cube icon by the side>you will then see the following option i."logged in with facebook" ii. "Platform" iii. "Apps other use" iiii. "Old versions of facebook for mobile". These is strenuous part, go to "logged in with facebook" option click the apps one by one and select "remove" after these go to "platform" select "NO" for "game invites and application" and them select "edit" and then "turn off platform" OR
2.if you can't go true that stress, simply go to "platform" and select "NO" for "game invites and application" and then select "edit" and "turn off platform". Also go to "apps other use" and disable it. You should see something like this. 

For other browsers just look for "account settings" and you will find the accompanying option I mentioned earlier.
 NB: you cannot use the facebook application, you have to use your browser.
Btw, don't mind the mistakes and errors in my write-up...You can thank me later, and please don't forget to share.
.
.
.

Source: Me.