Are we allowed to watch Indian songs and English movies in which the performers are often half nude? If yes, how big sin is this? Is it a grave sin or a minor one? How can one prevent indulging in these sins? Though I offer my prayers regularly yet these things attract me very much. I just watch the song. I promise myself not to watch again but fall prey to the snares of Satan again and again. You know devil will not leave us to grave according to Islam.
Watching a movie per se is not haram, however if the movie contains scenes or themes that pollute one's sole and heart then it will become haram to see those scenes or to be entertained with those themes. One of the important elements of taqwa in Islam is haya (to feel uncomfortable when facing a scene or situation that is not in accordance to modesty). Not observing this attitude can easily bring us to the situation where committing sin becomes routine and normal. The Qur'an advises believers to cast down their looks (24:30). This definitely applies to the case you illustrated.
If you have a habit of watching scenes and movies that you know are not appropriate for a believer to watch then you should try to replace this habit with good habits. Committing sin takes away our interest in worshiping God and the joy and the pleasure that comes with it and after it. This however works the other way round as well, that is, sincere worshiping of God takes away our interest in committing sin and the joy that comes with it. My humble advice (as one who himself needs much advice) is to try to improve the quality of your prayers as a good prayer is one that prevents you from such sins (Qur'an, 29:45). Also try to do more prayer and read the Qur'an a lot.One of the effects of this will be that it will help you appreciate and whole heartedly recognize that God is with you and He sees all that you are doing. Realization of this fact is enough to stop a person from committing sin. Of course socializing with God fearing people, exercising and filling out your free time with Islamically appropriate entertainments also help a lot.
Any sin that is repeated to the extent that becomes like a habit can be categorized as a major sin. This is because repeating a sin over and over (while knowing it is a sin) is most of the times an indicator of the rebellious and arrogant attitude of the sinner. Of course the door of repentance is always open for a servant of God, even if he has committed a major sin.