Universiade or universiad

Your question is almost incomprehensible. Olympiad derives directly from its Greek original. I have never seen the word ended with an "e" and consider it to be a mispelling. I have never seen such a word as "Universiad." If it does actually exist, i would consider that it is a "back formation" from Olympiad. The Greek formation (which was Latinized) -idae means "from the family of." So an Olympiad is an event from the family of such events, which first took more than 2500 years ago. Specifically, in modern usage, it has come to mean the four year period preceding each occurrence of the Olympic games.

The use of the suffix -idae or simply -id can be seen in such words as arachnid, meaning spiders, and deriving from the fable of Arachne, the girl who was turned into the first spider by the Greek goddess Athena. Today, members of the genus of spiders are referred to as arachnidea, or simply as arachnids--and meaning that they are members of the family of Arachne. People alleged to be descendents of Hercules (the Latin form, in Greek he is called Herakles) would be called the Heriklidae, or simply the Heraklids.

I can see how this would have been applied to the four year cycle of Olympic games, since the ancient Greeks conducted a series of competetive events over the four year period to determine who would participate in the games. But i can't think what anyone would mean by "Universiad," given that either universe or university have significantly different and broader meanings than that of a group of athletic competitions.

If you have read this somewhere, you need to give us some context.

You may be trying to mix some Spanish words in with English, Universidad maybe?

The modern Olympiad is a period of four consecutive calendar years, beginning on the first of January of the first year and ending on the thirty-first of December of the fourth year. The Olympiads are numbered consecutively from the first Games of the Olympiad celebrated in Athens in 1896. The XXIX Olympiad began on 1 January 2008.

"Olympiade" is the spelling of the equivalent word in a number of different European languages including German, French and Dutch, and Olympiada is the Spanish word.

As Setanta notes, spelling the word with a final 'e' constitutes a misspelling in English. He says he has never seen the word "Universiad". He might well see the word "Universiade" if he looks around sufficently widely, and discover that it refers in a number of languages to an international multi-sport event, organized for university athletes by the International University Sports Federation (FISU). The name is a combination of the words "University" and "olympiad". The Universiade is often referred to in English as the World University Games or World Student Games.

The Asiad is a four-yearly multi-sport event held in Asia.