Swamiji has quoted great verses in support that waking state karma does not get meted out in dreams state. But as moonstar2001 has commented, there are differing views on this.
Since you mentioned Sri Swami Sivananda's quotes, let us see what the great saint Sri Swami Sivananda Himself has said about this:
Does dream actions result in karma getting generated?
Sri Swami Sivananda says in 'Dream' by Sri Swami Sivananda
The dreamer is not affected by any result whatever of the good and the evil he sees in the dream state. Because in dream the dreamer does not actually do what is holy or evil, he is not chained by either; for, good or evil actions and their consequences are not imputed to the mere spectator of them.
No one regards himself a sinner on account of the sins committed in dreams. Nor do people who have heard of them condemn or shun the person on that account. Hence he is not touched by them.
That is He tells us that dream actions do not result in karma in waking state. However do they result in karma in dreaming state? That is a great question. However that is unrelated to this question so let us not digress.
Does real-world karma affect us in dreaming state?
Sri Swami Sivananda in 'Dream' by Sri Swami Sivananda:
The dream objects are created by the Lord as fruition of the minor works of the Jiva. In order to reward the soul for very minor Karmas, the Lord creates the dreams.
The Universal Soul is the creator of dreams and not the individual soul; for, had it been possible for the latter to shape his dreams, he would never have dreamt a bad dream, but would always have dreamt only propitious ones.
Thus Swamiji says that basically the very minor karmas are meted out in dream state. However no new karma is created (in the waking world) because of actions done in the dream world.
In Mahabharata Anusasana Parva, Section VII (thanks Keshav for the link), Bhishma says that fruits of those actions done with the mind are experienced in dreaming state while those actions done with body are experienced in waking state:
for example, the fruits of actions done with mind are enjoyed at the time of dreams, and those of actions performed physically are enjoyed in the working state physically.
How about Susupti or deep sleep state? Does any karma get meted out there?
In deep sleep there is nothing but undifferentiated mass of conciousness. There are no desires, no objects to enjoy and no actions that can be performed. Thus there can be no karma either generated or meted out.
Mandukya Upanishad verse 5
The third quarter is prājña, where one asleep neither desires anything nor beholds any dream: that is deep sleep. In this field of dreamless sleep, one becomes undivided, an undifferentiated mass of consciousness, consisting of bliss and feeding on bliss. His mouth is consciousness.
Basically in conclusion, everybody agrees that actions performed in dreams do not generate any karma, however with respect to waking state karmas affecting dream state, some saints say that minor karmas do get exhausted in the dreaming state while others say that they do not.
Is sleeping itself result of karma?
Well sleeping is because of partial exhaustion of karma. That is when the jiva in waking state performs all actions and eventually Mind and body gets exhausted by experience. That causes sleep.
Ofcourse this is obvious and no reference is required for this! But still just to follow site guidelines, Sri Swami Sivananda describes the philosophy of sleep by Sri Swami Sivananda:
Just as a kite which flies up in the sky at the dawn of the day and roams about here and there in the high regions in search of food throughout the day, takes complete rest in its own nest on the tree at night, so also the Jiva or the individual soul after having wandered in the dense forest of sense-objects all day long, gets into its abode called the Karana Sarira and enjoys the bliss of Sushupti or deep sleep.