tuning confusion

So I've had my Lanikai LU-21 Tenor for a few days now, came with some nice Aquila strings. Though I've been having problems with tuning it correctly.

In one method, I tune to the regular GCEA, and when I tune each string in the open position with my own tuner and with http://www.get-tuned.com/ukulele_tuner.php , it sounds just fine.

In another method, I'll just tune the C string with an electronic tuner, then hold down the 7th fret to tune the G to, and do that for the other strings. The problem is, when I use this method, playing the now-tuned strings openly makes them sound out-of-tune.

If I tune with the first method, and play a G chord (0232), the G string and the E string are both playing SHOULD make the same sound, but they don't - they sound out of tune. But when I just play all the strings openly, it makes a perfect C6 chord sound.

Are my strings out of wack over just a few days of casual play, is it the poor build of the uke, is it detonation...I'm so confused

I guess If my above explanation is too much, I can simplify it. If I tune the G and C string, then play the 7th fret on the C string, both the G string and the fretted G note on the C string should sound the same...but they're slightly off.

I guess the only conclusion I can come up with is that because the length of the strings are greatly shorter than that of a guitar, even the slightest bend from simply fretting the string will cause it to be a little sharper than intended.

It sounds to me like you have an intonation problem. Basically as you move up the fretboard the notes go further and further out of tune. I'd test this with your electronic tuner, because the fixes are tricky. It could have to do with new strings just needing a week to settle, or it could be a number of things that are harder to address...for example, it could be that the action is too high, and it could be that the intonation is just a little off on your uke because the bridge is placed wrong or the frets, or a number of other things. The strings will fix themselves, the rest may be more trouble than its worth, and you might want to consider exchanging it. Sorry to be the bearer of bad news.

Have you checked it against a tuner? That sounds like one really bad intonation problem if its off, especially if the G note at fret 3 on the E string is out. I have a cheapo unmentionable Ashton UKe with a bent & twisted neck that's now an ornament, and even that is in tune for at least 3 frets. Maybe the strings will settle down, or perhaps a different set of strings might be worth trying.