I find it encouraging that you mention he cries only occasionally at day care and then usually when some child takes something from him. It appears that this generalized crying behavior occurs, ,for the most part with you at home. Time-outs are not going to accomplish much; they tend to be overused in situations like yours and no real alternatives really get developed. Yelling at him so you can be heard sounds rather futile also.
Right now, the three of you are locked in a behavioral pattern that needs to change; continuing your same responses and expecting different results from him is not logical. I think changes in his emotional responses will come far more readily if you change some of your responses. He is receiving considerable attention for his crying; this behavior has given him too much "power" and he doesn't know how to relinquish it. Unless he has some truly deep-seeded fear(s) that keep him on the verge of tears, he is having a difficult time breaking out of this secure crying pattern.
I would begin a change in your behavior pattern by focusing on two fronts. First, I would find many occasions when you are together with him or alone one-on-one to show your appreciation of him, physically and verbally; create situations where it's easy for you to praise him. Second, act in a rather paradoxical manner if he begins his crying. Here are a few paradoxical responses that can begin to break his rhythm: (1) When he begins to cry, ask him if he could cry louder right away because you have something nice you'd like to do with him and you don't want to wait too long to do it. (2) Tape record his crying and have the tape cued up so that when he begins you can press the button and hear him cry on tape; when he cries, play the tape and leave the room saying, "I wonder if we can tell which crying is (son's name) and which is the tape crying." (3) Designate a crying chair or cushion or spot on the couch or floor and say to him at odd times when he isn't crying, "You can go and cry there now if you want or you can do it later." All these suggestions may seem odd but I have used paradoxical techniques often in my practice with kids and seen their locked-in habits change. With changes from you he will change in time.