A rostrum is a platform that someone stands on to make a speech, like a stage.

A lectern is a support in a church on which the bible rests. In protestant churches it is often in the form of an eagle with spread wings.

A podium is a small platferm used to raise someone or something above the level of its surroundings. For instance, the conductor of an orchestra stands on a podium.

ROSTRUM:

A ram bow on a ship.

The platform a speaker stands on while giving a speech. Such platforms in the Roman Forum were made in the shape of a ship bow. The most famous one is the Rostra in the Roman Forum.

LECTERN:

A Lectern (from the Latin lectus, past participle of legere, “to read”) is a reading desk with a slanted top, usually placed on a stand or affixed to a some other form of support, on which documents or books are placed as support for reading aloud, as in a Scripture reading, lecture, or sermon. To facilitate eye-contact and improve posture when facing an audience, lecterns may have ajustable height and slant

PODIUM:

A podium (plural podia) is a platform that is used to raise something to a short distance above its surroundings. In architecture a building can rest on a large podium. Podia can also be used to raise people, for instance the conductor of an orchestra stands on a podium as do many public speakers. Additionally, podium has commonly come to mean the object a speaker stands behind, even when it is at floor level, though the proper term for that item is a lectern.

So, to put it simply, the first one is in the shape of a ship’s bow, the second one is a stand with a slanted top & the third one can be a soapbox or step that someone stands on.