hand around/round: Could one of you hand these drinks around? (To pass something to all the people present in a group)  

hand back:  We handed back the forms after filling them. (To return something to the same person who gave it out) 

hand down:  These stories and legends have been handed down from generation to generation. (To pass on from older to younger generation)

hand down:  Her pearl necklace was handed down from her grandmother. (To pass something on to a younger member of the family)
hand down:  The court handed down a life sentence. (To publicly announce a judgment)

hand in:  The students handed in their homework without being told to. (To give something to a person who is in a position of authority)

hand out:  The volunteers helped to hand out parcels of food to victims of the disaster. (To distribute)

hand over:  The captives were ordered to hand over their weapons. (To give up)

hand over:  Members of the crowd caught the pickpocket and handed him over to the police. (To pass control of someone to someone else)
hand over:  The receptionist handed my call over to the person in charge. (To pass responsibility for something to someone else)

hang around:  She spends her time hanging around with friends in the park. (To idle)

hang around:  He hanged around with the wrong people and ended up in prison. (To spend with someone)

hang back:  He is often advised not to hang back but to mix freely at school. (To be reluctant to do something because of lack of confidence or shyness)

hang on:  She asked me to hang on while she made a telephone call. (To wait)

hang on:  The standing passengers hung on tight as the bus went along a narrow, bumpy road. (To hold tightly to something)
hang on:  We were exhausted but we realized we had to hang on a bit longer as we were nearing the summit. (To continue in spite of difficulty)
hang on:  He believes the success of his public speaking hangs on his ability to speak effectively and clearly. (To depend on)
hang on:  The cult members hang on every word spoken by their leader as they have great faith in him. (To pay particular attention to)
hang on to:  Grandpa hangs on to his collection of stamps with the belief that they become more and more valuable as time passes. (To keep something)

hang out:  After school, he hangs out with his classmates in a snooker hall. (To spend a lot of time with someone at some place)

hang over:  The thought of her husband’s unfaithfulness never ceases to hang over her. (To mull the possibility of something happening)

hang together:  They hung together while waiting for the rescue team to find them. (To stick or stay together)

hang up:  She was so angry she hung up before I could explain. (To abruptly end a telephone conversation)

hang up:  Finally, she hung up after speaking for more than an hour.  (To replace the telephone receiver)

happen along:  We invited our former lecturer to join us for a drink when he happened along. (To be, come, or go to a place by chance) 

happen by:  We would have remained lost if we hadn’t happened by a souvenir shop selling street maps. (To find a place by chance)
happen on/upon:  He happened upon the key to his car just as he was about to give up his search. (To find by chance)
happen on/upon:  We were walking and chatting when we happened on a fat wallet on the pavement. (To come upon)
happen to: Whatever happened to those ducks that used to waddle along the river bank. (To have or seem to have disappeared)

hold against:  It was not totally his fault, so I can’t hold it against him alone. (To dislike someone for their past wrong or mistake)

hold back:  She struggled to hold back her tears. (To have control over something)

hold back:  He felt his lack of qualifications would hold him back from his well-deserved promotion. (To block one’s advancement)
hold back:  The police subjected him to further interrogation as they believed he was holding back some information. (To retain in one’s possession)

hold down:  Mick seems unable to hold down a job for longer than a month. (To keep a job)

hold down:  He wanted to beat up the other guy, and it took the two of us to hold him down. (To restrain someone)

hold forth:  For more than an hour, the speaker held forth on the inevitable end of the world. (To talk at great length)

hold off:  He always holds off making decisions until the very last moment. (To delay doing something)

hold off:  It was unexpected that, despite the looming dark clouds, the rain held off until after we arrived home. (To have not happened at once)
hold off:  They held the invading armies off until reinforcements arrived. (To avoid being attacked)

hold on:  He asked me to hold on and he will be out in a minute. (To wait for a short while)

hold on:  In the tug of war, the participants held on tightly to the rope and pulled it with all their might. (To maintain a firm hold of something)
hold on to:  We held tightly on to the rail as the bus sped on. (To grip firmly to something)
hold on to:  She held on to the national title for the second year running. (To retain possession of)

hold out:  The supermarket held out the chance for customers to win a brand new car. (To offer)

hold out:  They could not hold out the fort as reinforcements arrived late. (To defend or continue to resist)
hold out:  Will the food hold out through the winter? (To last)
hold out:  The financial leaders are not holding out any hope of a quick recovery in the national economy. (To offer the prospect for the future)
hold out for:  The other party is not holding out for a compromise, but instead insisted they are the legal owners of the land. (To accept something less)
hold out on:  Why do you hold out on me all the things I need to know? (To desist from providing information)

hold over:  The match was held over because of the snowy conditions. (To postpone)

hold over:  The film was unexpectedly held over for a couple of months. (To extend the duration of the showing of a film)

hold to:  The home team held the away team to a 2-2 draw. (To manage to achieve a draw and nothing more against an opponent)

hold to:  She held to her religious beliefs despite marrying someone from another religion. (To remain faithful)

hold together:  The different factions within the party are held together by a charismatic leader. (To remain united or mutually loyal)

hold up:  We arrived late as we were held up by traffic jam. (To delay)

hold up:  The gang held up a money changer at gunpoint before fleeing with huge amounts of different currencies. (To rob someone using the threat of violence)
hold up as:  The Governor was held up as a model of integrity and decency. (To use as a model)