How to call certain kinds of tall shoes that women use to wear?

Those are platform shoes; see pictures. (I don't know of a funny name for them, except that some similar shoes are called ho shoes .)

Platform shoes with spikes are sometimes called ankle breaker shoes or ankle breakers.

If you refer to shoes like those in your picture as stilts, yes, that will be perceived as humor. Ballasts will not be so perceived, since its usual meaning is as a weight or as a fluorescent light control.

The picture the OP gave. We call those stripper shoes.

And you are damn right I have sources. Put the dollar in my shirt.

And since these particular stripper shoes are black, as suggested by @Janus Bahs Jacquet, dominatrix shoes works here too.

Your grandma wears stripper shoes...

Flickr accepts stripper shoes...

My girl wears stripper shoes...

I would call them platform spike heels. Traditional platforms have, well, a platform under the ball of the foot as well as the heel, like these:

Here is an example of spike heel shoes:

Well, I'm hesitant to mention this but, in the UK at least, they are commonly known as 'fuck-me' shoes. Seriously. Wikipedia will tell you more!