Ukulele strings, too, should be changed.
As soon as the strings sound unusually dull or green/yellow discolouration appears, it's time to re-string your uke.
Otherwise, not only hygiene and sound are negatively affected, but the intonation may be lost, too. Ukuleles are strung similar to guitars, as both use synthetic-material strings.
Simply make a knot or a double loop, then lead through the bridge, keeping the tension. Thread through the mechanism, remembering to calculate enough length for coiling - two or three clean coils should be sufficient. If you stretch the string before tuning, the tuning will hold better.
The action can be adjusted through the bridge inlay and the nut grooves.
To do so, take the inlay out of the bridge after unwinding the strings somewhat. File the bottom part of the inlay until you have reached your desired level.
If the action is high in the top frets, the string has to be taken out of the nut groove which then has to be filed down a little.
Perfect action is the precondition for faithful intonation.