Cloud: is simply an aggregate of computing power. You can think of the entire "cloud" as single server, for your purposes. It's conceptually much like an old school mainframe where you could submit your jobs to and have it return the result, except that nowadays the concept is applied more widely. (I.e. not just raw computing, also entire services, or storage ...)
Grid: a grid is simply many computers which together might solve a given problem/crunch data. The fundamental difference between a grid and a cluster is that in a grid each node is relatively independent of others; problems are solved in a divide and conquer fashion.
Cluster: conceptually it is essentially smashing up many machines to make a really big & powerful one. This is a much more difficult architecture than cloud or grid to get right because you have to orchestrate all nodes to work together, and provide consistency of things such as cache, memory, and not to mention clocks. Of course clouds have much the same problem, but unlike clusters clouds are not conceptually one big machine, so the entire architecture doesn't have to treat it as such. You can for instance not allocate the full capacity of your data center to a single request, whereas that is kind of the point of a cluster: to be able to throw 100% of the oomph at a single problem.