Kriya is translated as activity, or action, and sometimes work. It does not mean work, however, in the same context as karma yoga when it is translated as work. One of the biggest proponents of ‘Kriya Yoga’ is Paramahamsa Yogananda and the various organizations that came about from his work. In his book, Autobiography of a Yogi, Chapter 26, he says:
The Sanskrit root of Kriya is kri, to do, to act, and react; the same root is found in the word karma, the natural principle of cause and effect. Kriya Yoga is thus ‘union (yoga) with the Infinite through a certain action or rite.” A yogi who faithfully follows its technique is gradually freed from karma or the universal chain of causation.
Upon analysis, its not different from the other yogas and can be thought of as a blend of jnana, karma, bhakti, and raja yogas. In the Complete Works, In Raja Yoga, Swami Vivekananda refers to Kriya as ‘…work, working towards Yoga.’ Sometimes Kriya can refer to rituals associated with the worship of God, and sometimes it refers to Yama and Niyama, which are considered the preliminary steps to Yoga. Patanjali says in his Yoga Aphorisms II.1-2 (available here, Volume 2, under the heading Raja Yoga - http://www.advaitaashrama.org/cw/):
Mortification, study, and surrendering the fruits of work to God are called Kriya-yoga.
(It is for) the practice of Samadhi and minimizing the pain-bearing obstruction.
Hatha Yoga refers to the physical exercises and postures. Besides the postures, it will usually include some of the practices of Raja Yoga, including pranayama, but the greater emphasis is on the physical postures. The Hatha Yogi desires to arouse the Kundalini, not for purposes of Liberation, but for the purpose of attaining siddhis. The ‘powers’ that an accomplished Hatha Yogi attains are some of the siddhis described in Patanjali’s Yoga Aphorisms. Attainment of these siddhis does not bring Liberation. In his book Shakti and Shakta, Arthur Avalon (Sir John Woodruffe) says:
…But it may be said, the Hatha-yogis do get sick and die. In the first place, the full discipline is one of difficulty and risk, and can only be pursued under the guidance of a skilled Guru. As the Goraksha Samhita says, unaided and unsuccessful practice may lead not only to disease but death. He who seeks to conquer the Lord of Death incurs the risk, on failure, of a more speedy conquest by Him. All who attempt this Yoga do not of course succeed or meet with the same measure of success. Those who fail not only incur the infirmities of ordinary men, but also others brought on by practices which have been ill pursued or for which they are not fit. Those again ho do succeed, do so in varying degrees…All have not the same capacity or opportunity, through want of will, bodily strength, or circumstance. All may not be willing or able to follow the strict rules necessary for success. Nor does modern life offer in general the opportunities for so complete a physical culture. All men may not desire such a life or may think the attainment of it not worth the trouble involved. Some may wish to be rid of their body and that as speedily as possible, It is therefore said that it is easier to gain Liberation than Deathlessness.
In the Gospel of Sri Ramakrishna, He says (Chapter 11, With the Devotees at Dakshineswar (I) available here - http://www.ramakrishnavivekananda.info/gospel/gospel.htm):
There are two kinds of yoga: hathayoga and rajayoga. The hathayogi practices physical exercises. His goal is to acquire supernatural powers: Longevity and the eight psychic powers. These are his aims. But the aim of rajayoga is the attainment of devotion, ecstatic love, knowledge, and renunciation. Of these two, rajayoga is the better.
And in Chapter 13, The Master and M., he says:
"People practise various Tantrik disciplines to acquire supernatural powers. How mean such people are! Krishna said to Arjuna, 'Friend, by acquiring one of the eight siddhis you may add a little to your power, but you will not be able to realize Me.' One cannot get rid of maya as long as one exercises supernatural powers. And maya begets egotism.
"Body and wealth are impermanent. Why go to so much trouble for their sakes? Just think of the plight of the hathayogis. Their attention is fixed on one ideal only — longevity. They do not aim at the realization of God at all. They practise such exercises as washing out the intestines, drinking milk through a tube, and the like, with that one aim in view.
"There was once a goldsmith whose tongue suddenly turned up and stuck to his palate. He looked like a man in samadhi. He became completely inert and remained so a long time. People came to worship him. After several years, his tongue suddenly returned to its natural position, and he became conscious of things as before. So he went back to his work as a goldsmith. (All laugh.)
"These are physical things and have nothing to do with God. There was a man who knew eighty-two postures and talked big about yoga-samadhi. But inwardly he was drawn to 'woman and gold'. Once he found a bank-note worth several thousand rupees. He could not resist the temptation, and swallowed it, thinking he would get it out somehow later on. The note was got out of him all right, but he was sent to jail for three years. In my guilelessness I used to think that the man had made great spiritual progress. Really, I say it upon my word!
…"A true devotee of God does not care for such things as wealth or health. He thinks: 'Why should I practise spiritual austerities for creature comforts, money, or name and fame? These are all impermanent. They last only a day or two.'"
In his book, The Spiritual Heritage of India, Swami Prabhavananda says in a footnote:
The posture as taught by Patanjali has nothing to do with the postures and practices mistakenly associated with the word yoga.
And in another footnote:
I have purposely refrained from giving the breathing exercise known to the yogis, for they should never be practiced without previous instruction from an adept teacher. Many books published in America on the subject of yoga describe breathing exercises which are not the pranayama as taught by Fatafijali, but rather that belonging to the school of hatha yoga. I am certain that those who write indiscriminately of yoga breathing exercise do much unintentional harm. For these exercises are dangerous to the beginner without the proper personal guidance. Furthermore, it is my opinion that the many varieties of breathing exercises that taught by hatha yogis are dangerous even when practiced under the supervision of teachers skilled in hatha yoga. They may sometimes aid in building the physical body, but they just as often injure the brain. There are instances in Indai, to my personal knowledge, of men who have become mentally unbalanced by such practices. Unfortunately an interest in breathing exercises that go by the name of yoga has been created in America by irresponsible teachers and authors.
In the Uddhava Gita XXIII. 41-42, Sri Krishna says (Swami Madhavananda translator):
There are some strong-willed people who by various means first make the body very strong and of undecaying youth, and then practice Yoga with a view to acquiring extraordinary powers.
But that is not praised by the wise, for such effort is useless, since the body is mortal, like the fruits of a tree.