Sthira karakas include only 7 planets because only they have physical bodies. They are presided by Shiva. As Shiva presides over death, they show the destruction of body. Sthira karakas are useful in timing the death of various near relatives.
List of Sthira Karakas:
Sun or Venus (stronger): Father
Moon or Mars (stronger): Mother
Mars: Younger siblings, brother-in-law and sister-in-law (spouses of siblings)
Mercury: Maternal relatives (uncles and aunts)
Jupiter: Husband, sons, paternal grandparents and other paternal relatives (uncles and aunts)
Venus: Wife, father-in-law, mother-in-law & maternal grandparents
Saturn: Elder siblings
Some people opine that Sun should be taken as the fixed significator of father for daytime births and Venus for nighttime births. Similarly, Moon is taken as the fixed significator of mother for nighttime births and Mars for daytime births.
The use of sthira karakas has already been explained. They are presided by Shiva and they are used in the timing of death of the above relatives. They should not be used in general predictive astrology in the place of naisargika karakas. For example, some astrologers use the 7th from Jupiter instead of the 7th from Venus to predict marriage. However, Venus is the natural significator of marriage and the 7th from Venus should be used for predicting marriage, both in male and female charts. When predicting the death of spouse, we use Jupiter in female charts and Venus in male charts.
Another difference between sthira and naisargika karakas is that sthira karakas themselves represent the physical bodies of the relatives. In the case of naisargika karakas, we must take the relevant house from the karaka. For example, Jupiter represents the physical body of husband in a female chart, for the purpose of timing death. For the purpose of timing marriage, the 7th from Venus (and not Venus himself) shows husband.
Chara karakas are also similar to sthira karakas in this aspect. We do not take the 7th from DK for spouse, but DK himself shows spouse.