To unlock Cloud strife, you must first See the cut scene where Mustadio's Father assembled the parts he found and build a dimension transporter then he will he say you have to find another zodiac stone "the Cancer stone". You must travel to Zeltenia Castle. then Go to the Tavern , then rumors select the last rumors, i forgot the name but its about the Nelveska Temple being guarded by a iron sentinel who kills anyone that goes to that place. After selecting that rumors a route to Mevleska Temple will appear then go to Nevleska Temple after that you will have to fight Construct 7 and defeat him. after that you will acquire the cancer stone. After that travel to Goug a cut scene will be shown where the transporter will transport Cloud to Ramza's dimension. Cloud will not yet join your party but leaves. You must then travel to Sal Ghidos there you will find Cloud and you have to fight and if you win Cloud will then join your Party.
If you also have Beowulf and Reis the holy dragon in your party a cut scene will appear then Reis will be transformed into a human and now can now learn Skills and wear items.