When Can I Use These Chords?

Since all of the previously illustrated voicings have the same notes as a "normal" minor chord, you could theoretically insert any of them at a time a minor chord was required. This is where personal preference becomes your guide; some guitarists will elect to use these shapes all the time, while others will use them more sparingly.

How Do I Use These New Chords Effectively?

To start using these new minor chord voicings to their fullest effect, you're going to have to spend a lot of time getting comfortable with them. A goal to set for yourself is to be able to move smoothly from one chord to the next in a progression. This will often mean moving from a root position chord to a 2nd or 1st inversion chord, a concept quite difficult to master at first.
We'll use the classic Santana tune Black Magic Woman as a foundation for examining the basics of voice leading minor chords.

Since the song has only three chords: Dmin, Amin, and Gmin, the process will remain fairly simple. We'll start by choosing a voicing for the Dminor chord. This voicing will dictate which voicings we'll play for both the Amin and Gmin chords. The first example starts with a 2nd inversion Dmin chord voicing.

The 2nd inversion Dmin chord in the above example moves most smoothly to the root position Amin chord. The Dmin chord also moves most easily to the 1st inversion Gmin chord.

This second example starts on a 1st inversion Dmin chord. This voicing moves most smoothly to a 2nd inversion Amin chord, and a root position Gmin chord. These are just several of the chord voicing possibilities you could use in playing Black Magic Woman. Experiment with others, making sure, when switching chords, to move to the closest available voicing on the same string group.
The above exercise should not be considered a musical rule. There is nothing saying you have to always move to the closest available voicing. But, it makes good musical sense, and is pleasing to the ear. Do not feel the need to stay on one voicing for the duration of the chord. You could play four different voicings for Dminor in the first four bars of Black Magic Woman alone. The key is experimentation; in order to master minor chord voicings, you'll need to play them extensively.

Now, on to the final step: Minor chord practice tips.