call around means phone many different people, or to visit someone’s house (e.g. I called around but there was no place to book our party.)

call back means return a phone call or to return to see someone (e.g. Can you please call me back when you are available.)

call in means 1) to visit somebody for a short time without arranging (or drop in) (e.g. I called in but you were not in.) 2) to phone (e.g. I called in all morning to the internet company.) 3) to ask someone or company to come and fix (e.g. We must call in a technician to fix out internet problem as soon as possible.) 4) to ask someone to give you something (e.g. I have no choice but to call my parent in for the house loan this month.)

call on/ upon means to ask formally for someone to do something (e.g. We have to call on the government to help.)
call on someone means ask for an answer or visit someone (e.g. The teacher called on me for questions.)
call on something means to decide to use something (e.g. We may need to call on professional support.)

call off or call something/ someone off means to decide not to have something or cancel it because it is no longer possible (e.g. If there was much more rain, they've had to call off the match. Tom called the wedding off because he changed his mind.)

call up someone or call someone up 1) means to phone someone (e.g. Give me Ann’s phone number. I will call her up and say thanks.) 2) to join army or to play in a sports team (e.g. My father was called up at the beginning of the war.)

calm down means relax after being angry or excited (e.g. You should calm down before you take an examination. Keep calm and study! Keep calm and eat! Keep calm and carry on!)

care for someone/ something means 1) like or love (e.g. I don't care for his behaviour.) 2) to protect or provide something (It’s good to know that the children are being cared for by neighbours at their home.)

carry on means to continue doing something (e.g. Our family moved to the UK to carry on children’s study)
carry on with means just carry on with what you were doing at that time (e.g. Carry on with your work until lunch is ready.)

carry out means to complete something, an order, a survey/ an investigation/ a plan etc. (e.g. An investigation into the accident will be carried out a thorough search of the premises as soon as possible.)

catch up means to reach the same progress or standard (e.g. I was off for a while, it may be hard to catch up in this week.)
catch someone up means move faster that someone in front (e.g. You'll need to run faster, if not, you will never catch him up.)

chase up something means to find something that is needed (e.g. I was a responsible person for chasing up late replies.) 
chase someone up means to ask someone to do something (e.g. If we want to go for a summer vacation, we have to chase ourselves up.)

check in means arrive and register at a place or to contact someone by making an appointment (e.g. Please check in at least an hour before departure.)
check someone or something in means to deal with someone when you arrive (e.g. The receptionist checked us in. We checked in our luggage and went through security after they checked our luggage in.)

check out means leave a place after a payment made, or to get information or to examine before use or taking (e.g. We have to check out of the hotel before midday. I had already checked out the new restaurant.)
check out someone or something means look at (e.g. The company checks out all new business opportunities.)
check someone or something out means look at carefully (e.g. All students must check us out anytime online before submitting the application.)

chip away at means to gradually make something less effective (e.g. It's hundreds of illnesses that we chip away at.)
chip in means to interrupt a conversation (e.g. If you have any question, you can chip in any time.)
chip in something means to help or share something (e.g. If you chip in your time and money, we will have a very nice party tonight.)

clear up/ clean up/ tidy up something means to make a place completely clean and tidy. (e.g. We need to clear up before we go out. When are we going to tidy up or tidy a place up?)
clear up means become bright weather or to make a lot of money (e.g. It was raining when I got up, but it cleared up now. I cleaned up at the last night gamble.)

close down or close something down/ shut down means stop doing business (e.g. There used to be local shops at this street. They are closed down recently.)
close up means move closer together or become emotionless or blank (e.g. She doesn’t like the movie and her face close up sadly.)

come across something means find unexpectedly or find by accident, or express clearly (e.g. I came across my old reports when I was tidying the closet. I come across in this photo is a great sense of happiness.)

come apart means separate or to break into several parts (e.g. The top and bottom come apart I picked up the book.)

come back means to return to a place (e.g. Jon is leaving tomorrow and coming back on next Sunday.)

come down means become lower or to fall and land on the ground (e.g. House prices are not come down yet.)
come down to something means to be the most important (e.g. Eventually, it all comes down to is either I am a rich or I leave.)
come down with something means become sick (e.g. My nephew came down with bad flu last holidays.)

come forward means to offer to give help or give evidence (e.g. The woman came forward with information relating to her husband's appeal.)

come from place means originate in, birth or made in (e.g. The theory of origami comes from England.)

come over means to come to a place, move from one place to another, or to seem to be a particular type of person. (e.g. Why don't you come on over to the UK this summer? I interviewed and felt she came over as a qualified person.)

come up means appear, to move towards, or be introduced in a conversation (e.g. Something's came up at work during our meeting yesterday.)
come up against means encounter problems or difficulties (e.g. If you come up against difficulties, let me know.)
come up with a suggestion means think of a solution (e.g. Ann is very creative. She's always coming up with new ideas.)

count on/ upon somebody/ something means rely on or to expect something to happen (e.g. I am counting on you to make dinner before I arrive home. I didn't count on being held up in the traffic, but you had to count on it.)

cross out/ cross something out means draw a line through on wrong information (e.g. Please cross out any wrong information and write correct them.)

cut back means to turn back or reduce (e.g. We should request to cut back production because the global warming impact.)
cut back on something means to spend less, do less, or use less of something (e.g. My doctor wants me to cut back on sweets and salty foods.)

cut something down means shoot or make something fall to the ground (e.g. John is used to work over 60 hours per week even though he’s trying to cut it down.)
cut down on something) means eat, drink or do something less often (e.g. I'm trying to cut down on caffeine. I eat too much of it)

cut in means interrupt by saying something, or start operating, usually automatically, or come in too closely in front of another vehicle (e.g. Your father cut in while I was talking to minister. The air conditioner cuts in when the temperature rises to 20°C. The bus driver got angry when that car cut in. (on us/in front of us))

cut somebody off means take out of a will (e.g. My grandparents cut my father off when he remarried.)
cut something off means remove with a sharp tool such as a knife, or to stop providing something such as utility etc. (e.g. Cut the tops off the carrots. The electricity supply company will cut off power when we don’t pay the bill on time.)

cut out means stop working (e.g. Our car was cut out at the green traffic light.)
cut something out means to remove part of something, or to remove something unnecessary or unwanted it completely from a situation (e.g. I cut this photo out of the newspaper.)