I'm glad to answer your question and I hope it'll be useful.
All 3 exams you listed are recognized by the Italian Ministry of Education. This means they all allow foreigners either to work or get enrolled in Italian Universities. I will specify some details about each exam.
CELI is supplied by the University for Foreigners of Perugia. There are 6 levels based on the Common European Framework or Reference for Languages (CEFR): CELI Impatto (A1) - CELI 1 (A2) - CELI 2 (B1) - CELI 3 (B2) - CELI 4 (C1) - CELI 5 (C2). Levels C1 and C2 allow you to be almost equivalent to a native speaker. You can take the exam in different sessions. Here is the calendar for next year: http://www.cvcl.it/categorie/categoria-129
CILS is supplied by the University for Foreigners of Siena. Again, there are 6 levels based on the CEFR: CILS A1 - CILS A2 - CILS UNO (B1) - CILS DUE (B2) - CILS TRE (C1) - CILS QUATTRO (C2). The calendar of those exams is available at http://cils.unistrasi.it/82/13/Le_date_degli_esami_%28sedi_italiane_ed_estere%29.htm
PLIDA (Progetto Lingua Italiana Dante Alighieri) is supplied by Società Dante Alighieri, dedicated to the greatest Italian author Dante. As usual, there are 6 levels depending on the CEFR. There are more sessions throughout the year. Here you have the calendar for 2015: http://plida.it/plida/images/stories/documenti/2015/Date_PLIDA_2015.pdf
All exams will test you on the four abilities: listening, speaking, reading and writing. If you are at a good level of Italian, I highly suggest you to take indifferently one of them, though probably CILS and CELI are the most common.
Let me know if you need any further clarification, and please visit my teacher profile for information about the preparatory courses.
Have a great night!