Well....We have heard from all of you. Man, I'm scared just reading most off this.
There are are up to FOUR possible reasons for this. And they are somewhat related...
#1 The most likely is as mentioned, neck back-bow happened.
- This could be because OP switched to lighter strings
- It could also (not probable, but possible) happen because OP removed all the strings and the neck over-responded and didn't come back to original spot even with same gauge
Check: The bow in the neck that can prevent buzz is called "relief" if you fret the 6th string (or any) at the first fret with your left hand, and at the fret where the neck meets the body with your right hand pinky, you can very carefully pluck the string with the right hand middle index finger. If it make no sound, back bow. If it buzzes, you need to loosen the truss a little, if you can see a whole lot of space between the string and the frets around the 7th fret, you might tighten it a little.
SOLUTION: Loosen the truss rod 1/4 turn at a time, tune the strings, check for buzz. If you have to really force the turn, don't. Suggestion - loosen 1/4 turn (just to get rod moving) check for more buzz, tighten 1/4, then tighten (actually tightening now) another quarter.
#2 Something wacky with the action / bridge when the strings came off. The action could be impacted when you move the truss anyway.
- If the truss is too tight, the strings will raise higher off the neck. Often after adjusting the truss the strings can bee too high/too low.
- Loosening the Truss often lets the string rise too high
- Tightening can bring them too low.
Check: Play the notes, each string and see if there is buzz, or if ti just feels excessively high. Measuring at the 12th fret with a precise ruler is also ok. Height at the 12th fret is typically about 6/64th of an inch (2.38mm) on the bass side and 4/64th of an inch (1.59mm) on the treble side. Some may find this too high or too low, or not right depending on string gauge etc....
SOLUTION: Carefully adjust the bridge up or down very slightly. depending. Again, in your situation a little loosening of the truss will likely bring things back to happy. But, if you went lower gauge, you may adjust the truss a little looser than it originally was. The strings could end up slightly higher. Thus, lower them ever so slightly. Think 1/8th of a turn at at time, or adjust to the suggested height.
***INTERACTION ALERT: Remember, when you LOWER the action, the tension on the strings loosens. That will allow the neck to bend backwards. Be sure to tune to pitch after lowering, and before checking all the notes for feel, buzz, etc.
***Bends fret-out: If you are bending notes on the 12th or higher frets, this can happen because of the neck radius. Tight radius necks (like 12" on old Strats) can really have a problem with this and will need higher action.
#3 If a couple rounds of that do not get you to a good place, then the nut might be too low. A truss adjustment *might* help, but maybe not.
Check: Hold the string down at the third fret, see if the string hits the first or second frets. If so, you may need to raise the nut slightly, or get a new nut.
SOLUTION: An option is to put a very thin slip of paper, or cardboard, or flattened toothpick or anything under the nut and set it back in place. You can often place a nut with out glue. If you do use glue, use on a very little. Make sure it is right before you do that! A little sideways tap usually pops them off. Warning - they can break. Of course, after replacing the nut goes what? #1 and #2 all over again. Or, take to a tech or learn how to cut nut slots. I'll recommend get this done by someone. It requires nut blanks and some funky little files. It is totally doable, and not expensive, but kind of a little more than level 1 setup, and requires special tools.
#4 Now - this is a long shot, but it CAN happen. You may have had some frets raise up. I believe this is more often a high end of the neck thing, but could happen anywhere. When the truss bends an large amount, sometimes an ill-seated fret can raise up a bit, especially if it was back bow.
Check: If after checking all of that and adjusting a few rounds...you still have buzzes going on - adjust the truss so that the neck is perfectly flat. If you can't lay a straight edge on it without it rocking there is a raised fret or frets somewhere.
SOLUTION: If you are feeling frisky, gently tap the offending fret back in with a soft surface covering it and a soft mallet. DO NOT tap on the strings over the frets!!!! That will make dead spots and result in needing a new fret. Also, over do it and you may need a new fret/fret job. Take it to a luthier if this seems needed or #1/2/3 didn't work.
I defer to the wisdom of those who do this for a living. I don't.
I will say that learning to adjust the truss, the action, and the intonation and check these things is well worth the time. It really only requires a screwdriver and patience. You will be able to adjust it to your perfection, which most half-@$$ed alleged techs won't do.