#1
Sometimes when you have a guitar with old strings ( or a lower end acoustic with a bad nut ), the strings have a tendency to stick to the nut when you're trying to tune the guitar. So the string will suddenly go from too low to too high. For several years I've been using a product called 'nut sauce' which seems to help. But for several years before that, I would use lithium grease ( as advised by my guitar teacher at the time ). The nut sauce seems to work a bit better and lasts longer, and comes in a tube with a thin nozzle for an easy application. The lithium grease comes in thick tubes ( or tubs ) and is therefore a little messy when applying, and works well for a few weeks and then seems do dry up, leaving behinds a build up of residue on the guitar nut...

BobbyCrispy :-)
#2
Graphite works well....Just scrape a soft pencil "lead" and work that into the slot.

However, a permanent cure is a properly-cut bone (or similar material) nut. No binding.
#3
The best cure is new strings and properly cut nut slots. When the strings start catching and making noise that's probably from rust caused by oils and salts in your fingers.

I use a #2 pencil to scratch a little graphite into the nut slots before putting each new string on, it helps with strings going out of tune from using the whammy bar and helps a lot if they start sticking because they need to be changed. If I can't get new strings right away I'll use some graphite. If my strings are that bad I'll try to replace them if I can, it won't be long till they start losing intonation too.

You can get some welding torch tip cleaners and carefully open up the nut slots a little, that may help too. Be very careful that you do not cut them any deeper, especially if they are already right.
Hmmm...I wonder what this button does...
#4
It could be that the nut slots are just not sized for your string gauge.
Be aware that how the strings come off the nut to the tuning heads is important, they should be straight as possible and has a lot to do also with string life. I've seen strings to the tuning heads wound on the wrong side causing too much side force coming out of the nut slots which will cause friction and damage the nut slots.
#5
sounds like wrong sized nut slots to me. regardless of quality of the nut and guitar, if the slots are too thin, the strings will sometimes stick and then let go and make weird noises and just suck to tune.
Quote by Skeet UK
I just looked in my Oxford English Dictionary and under "Acoustic Guitar", there was your Avatar and an email address!