To destroy something is to break it beyond possible repair. Annihilate and obliterate mean the same thing. To obliterate something is to destroy it until there are no traces remaining. Eradicate is like annihilate and obliterate, but is usually used to refer to populations. For example, you can eradicate an animal, disease, rebellion, race, mould etc. by destroying every single member of that group.

You may find this online dictionary useful: www.thefreedictionary.com