Technically, the two words should be pronounced differently /klooʊz/ and /klooʊðz/, however, many educated native speakers do indeed pronounce them the same. The "th" sounds are generally problematic for native speakers, and often get dropped in the presence of an s. Interestingly, "close," ( /kloʊs/) meaning "near," always sounds very different from the other two words you mentioned. No, do not say "change your cloth." lol.

No, not to me they are not. The 'th' sound in clothes should be sounded - your tongue should flick off the back of your teeth and/or upper lip to make it. 'Change your clothes' would refer to more than one garment, so would refer to (say) both pants and shirt. You cannot use it in singular form - you should refer to the the specific garment in that case.

Well, I am shocked. I am a U.S. native speaker. I pronounce the "th" in "clothes," perhaps not perfectly distinctly, but it is there. I wrote that they are not the same when pronounced by careful U.S. native speakers. Then I decided I should check a dictionary. ahdictionary.com lists klōz FIRST, klōthz SECOND. Their audio example is klōz. So, chemmie, in U.S. English, yes, it appears that most speakers pronounce "clothes" exactly the same way as the verb "close." On the other hand, http://www.oxforddictionaries.com/definition/english/clothes is showing only one pronunciation, the one with the th, and that's the one used in their audio example It is difficult even for a native speaker to pronounce the "th" distinctly--the tongue has to move a long distance quickly--so it is natural to pronounce the "th" weakly or not at all. I personally pronounce it weakly, but it's there. If you can do it, I recommend that you try to use the British pronunciation because it is accepted in both countries.

I say them both the same.. LOL