I do not know how difference this meanings and how can i use in what situations ?
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Let's look at how these words are different.
The basic meaning is "relaxedly, unstressedly, in an easygoing manner".
First cited to 1907, making this a relatively recent term.
Derived from のびのび, in turn derived from verb のびる "to stretch out".
Think of a cat stretching out and relaxing.
The basic meaning is "slowly, unhurriedly".
First cited to 1563.
Structurally, would appear to be derived from ゆくゆく, but the meanings are almost opposite. That doesn't necessarily indicate unrelatedness: consider English terrible and terrific, ultimately from the same root, one with a very negative meaning and the other a very positive meaning. But the difference between ゆっくり and ゆくゆく is still puzzling.
One way to remember it might be to think of the word like 行【ゆ】く "to go", but slower, since you have that small-っ in the middle of ゆっくり.
The basic meaning is "to kick back, to relax".
First cited to the late 900s as a transitive verb, then cited in the Genji Monogatari a few decades later with the intransitive sense.
The original meaning was "to physically loosen something", extending then to "to loosen one's mood or mind", and then shifting to the intransitive sense of "to relax".
The way I memorized this one was thinking about くつ as "shoes" from the way you often take off your shoes after getting home, and then putting your feet up.
The verb くつろぐ is, well, a verb, so you can use it that way.
For the two adverbs, のんびり and ゆっくり, there is a lot of overlap. Broadly speaking, のんびり has more emphasis on "fun" or "easygoing", while ゆっくり has more emphasis on "slowly". You can say both のんびり歩【ある】く ("to walk in an easygoing manner") and ゆっくり歩【ある】く ("to walk unhurriedly"), and the meaning differs mostly in subtleties of mood. However, while you can say ゆっくり言【い】う ("to say something slowly"), it sounds a bit weird to me to say のんびり言【い】う ("to say something relaxedly"?). Perhaps if you're talking about someone who is really supremely laid back. :) Just make sure to use ゆっくり if you're asking someone to slow down when they're talking to you.
Please comment if the above does not address your question.