According to Sanatana Dharma, what are the types of sins?
What types of sins can be washed and how and in what cases it is not considered as sin even if people commit one?
The question seems simple, but it's a bit broad because there are hundreds of sins mentioned in our scriptures. There are so many kinds of sins mentioned in our scriptures that categorizing them would be difficult. Generally, a sin is committed when the prescribed laws of the sages are violated either by mind, body or speech:
varṇāśramaviruddhaṃ ca karma kurvanti ye narāḥ
karmaṇā manasā bācā nirayeṣu patantite [VP - 2.6.32]
He who through his mind, speech and action does work that is against his varnashrama dharma (duites as per his caste) falls into hell.
So one can say there are these three kinds of sins, viz. saririk (physical sins), manasik (mental sins), vachik (verbal sins). Nevertheless, scriptures do mention different types of sins as below:
Killing a Brahman, drinking liquor, theft, violation of the preceptor's bed.
Eating condemned food, giving up agnihotra, not fulflilling obligations towards gods, sages and manes, killing a woman, shudra or a vaisya, etc.
Beating a brahmana, smelling liquor or garlic, living through begging, etc.
Speaking untruth, serving a shudra, etc.
Killing worms and insects, stealing wood, fruit or flower, giving up patience, etc.
But apart from these there are hundreds of minor and major sins mentioned in the scriptures. And some are even equal to the mahapataka (mortal sins). Also, Mahabharata mentions about various kinds of sins including the five grave ones (mahapataka). They are as below in brief:
Drinking alcoholic liquors, killing a Brahmana, and the violation of the preceptor's bed, are sins that, if committed consciously, have no expiation. The only expiation laid down for them is death.
The unmarried girl who suffers her virginity to be deflowered incurs three-fourths of the sin of brahma hatya, while the man that deflowers her incurs a sin equal to a fourth part of that of brahma hatya (Brahmanicide).
By slandering Brahmanas or by striking them, one sinks in infamy for a hundred years. By killing a Brahmana one sinks into hell for a thousand years.
Sins committed cannot be just washed away without experiencing their corresponding punishment in hell. However, for sins committed unintentionally and in cases where the sinner repents his deeds [VP - 2.6.40], the scriptures prescribe performance of prayaschita (acts of expiation):
Sages prescribe a penance for unintentionally committed sins. Some declare, on the evidence of the revealed texts, (that it may be performed) even for an intentional (offence). [Manu - 11.45]
A man that has acted sinfully destroys his sin by acting virtuously afterwards and by penances. [Mbh]
Excluding the five grave sins (mahapatakas) that have been mentioned above, all other sins have expiations, provided for them. Expiating those sins according to the ordinances laid down for them, one should not again indulge in them. [Mbh]
A householder has five slaughter-houses (as it were, viz.) the hearth, the grinding-stone, the broom, the pestle and mortar, the water-vessel, by using which he is bound (with the fetters of sin).In order to successively expiate (the offences committed by means) of all these (five) the great sages have prescribed for householders the daily (performance of the five) great sacrifices. [Manu - 3.68,69]
To mention the various kinds of expiations mentioned in the scriptures for each type of sins would be too broad. However, along with expiations like vow of celibacy, living on begging, etc. all scriptures also mention remembrance of Vishnu's names and practice of devotion to Him as one of the best destroyer of sins. Bhagavad Gita also explicitly mentions it in the verse 18.66.
Sin is always considered as a sin whenever people commit it. One cannot simply knowingly commit a sin and think it will not be considered as a sin. In case of knowingly committing sin, the consequences and expiations are even more severe. But when a sin like death of someone occurs while treating other, while helping other (paropakara) or while punishing other, it is not considered as a sin [Agn Pu - 173.5]. Also, people who are God realized and perfectly situated in Self realization without the sense of doership, sinful acts like killing even do not bind them [BG - 18.17]
Agni Purana - 168, Mahabharat - 12.165
Garuda Purana deals with the list of sins that leads a human to Hell. I will take some verses from there and post them here.
5-12. Slayers of Brâhmiṇs, drinkers of intoxicants, slayers of owe, infanticides, murderers of women, destroyers of the embryo, and those who commit secret sins,
Those who steal the wealth of the teacher, the property of the temple or of the twice-born
Those who take away the possessions of women, and those who steal the possessions of children;
Those who do not repay their debts; those who misappropriate deposits; those who betray confidence; and those who kill with poisonous foods;
Those who seize upon the fault and depreciate the merit, who are jealous of those who have merit, who are attached to the wicked, who are foolish, who turn away from the company of the good;
Those who despise places of pilgrimage, good men, good actions, teachers and Shining Ones; those who disparage the Purâṇas, the Vedas, the Mîmâṁsâ, the Nyâya and the Vedânta;
Those who are elated at seeing the miserable, who try to make the happy wretched, who speak evil words, and are always evil-minded
Those who do not listen to good counsel nor even to the word of the Śâstras, who are self-satisfied, who are unbending, who are foolish, who thinks themselves learned;
These, and many others, very sinful, devoid of righteousness, certainly go on the Way of Yama, weeping day and night.