Modified - You can only use cards from the Modified format to make your deck, which currently is Ruby/Sapphire and up.
Limited - You can only use cards given to you at the Tournament to make your deck, for example the Team Rocket Returns prerelease. You are given boosters of the set and need to make a 40 card deck to play with, using the cards you pulled and basic energies that they have there.
Unlimited - You can use any cards from any sets of Pokemon to make your deck, except for any that were banned completely (Birthday Pika and Ancient Mew are the only ones I can think of).
Modified - Constructed - Same as Modified, the "Constructed" part is usually given. It means that you need to make a deck from your own collection of cards.
Modified - Limited - Same as Limited, I'm assuming. A Tournament where you get boosters of modified cards to construct a deck with.
Don't know the other two, and please, someone correct me if I'm wrong.