The things you have tried don’t effect your problems. 1.Is your intonation correctly set? 2.Do you stretch your strings after installing new ones? Especially on light gauges with plain G. 3.A lubricant like Stewart/McDonald sells for nut grooves help the strings have neutral tension (a must), but I have used pencil lead with good results. Only tune up to the pitch! Tuning down to note leaves slack in everything that will slip out of tune always. 4.Have you lost springs out of your tremelo mechanism? 5.Occasionally a set of strings are "funky" and can’t play "in". Hope this helps! Remember there is only two kinds of music (GOOD & BAD).