Is "Karmic Punishment" more effective? When I was young, my parents consistently used "Karmic Punishments", punishments that had a strong relationship to the misbehavior. They believed that this was more effective.

Examples:

Swearing or lying was punished by rinsing mouth out with soap
Physical violence was punished by spanking
Laziness was punished by physical labor.


Is there research to support the idea that relating punishment to behavior in this way is more effective than an unrelated but equally harsh punishment? Information about "Karmic rewards" is also valued.

Sidenote: My father also did this to train the household dog. Excessive barking meant being shouted at/gunshy training (loud noise) while biting was punished with a rap on the nose.
Its difficult to understand exactly which type of parenting style and discipline you experienced so please allow me to describe what I was able to find on parenting. 

There are many different styles of parenting. Authoritarian which are strict and rule based. Authoritative which has rules which are followed more responsive to the child's needs and feelings. Permissive which are the "lets be friends" type. Uninvolved which providing basic physical care without communicating or in some cases becoming neglectful. 

Each of these parenting styles tend to follow specific punishment outlines. 

Authoritarian parents tend to spank and say things like "Because I'm your parent. Because it is my house." rather than caring for the emotional needs of the child. Modern psychology never endorses spanking as healthy. Spanking teaches children to be aggressive. Possibly even associating such traits with love if a parent showed affection in association with spanking as is frequently practiced.

Authoritative parents provide guidelines for children to live by which are punished by a logical system of positive and negative punishment. A logical system of punishment is one where it follows from your behaviour that such actions could be eliminated and or added. The punishment fits the crime. For instance sass off toward the authority figure with a cell phone can lead to the loss of the cell phone. This would be a negative punishment where privileges are removed. A positive consequence for not doing laundry might be a fee for the laundry done that day. It adds the burden of a payment to the child. Sometimes bad behaviour can cause you frustration and its never appropriate to discipline a child while angry. Time outs are also an important healthy way to punish children. This is punishment by boredom so its important that the pre-established place be safe and uninteresting. In my experience a chair in the corner is more effective than the bed in the bedroom. Token economy a clear and consistent reward for behavior also works well. I never have experienced a situation where allowing a child to learn from their mistake by allowing "natural consequences" has worked well. Its labor intensive. Most parents simply use "natural consequences" as an excuse to by proxy harm/abuse, disengage or nag rather than prop up. 

Psychology also doesn't endorse the passive parent who never disciplines their child either or the extreme of the passive the uninvolved which abandons their child. 

The follow up to discipline is just as important as the discipline itself.

Like I said earlier with the information you gave its not possible to tell how healthy your punishments were. Its really not my place to judge your “Karmic Punishment”. From the descriptions I gave I think you can make up your mind.