You can find the different loss functions in the docs 32.
I assume you’ve already found the PyTorch tutorials 16 and would like to get started creating your own models.
There are a lot of good resources to learn more, e.g. Stanford’s CS231n for Visual Recognition 10 (with free Lecture videos), fast.ai’s course 6 (they use a high-level wrapper built on top of PyTorch) or Andrew NG’s coursera course 9.
For the beginning you could stick to the following (this is my biased opinion and the recommendations might not be the best for your use case!):

For regression, try nn.MSELoss() and no non-linearity for your model output. Also normalizing the target to [0, 1] or [-1, 1] might help.
For classification use F.log_softmax + nn.NLLLoss or no non-linearity + nn.CrossEntropyLoss.
Try optim.Adam as the default optimizer.
Try nn.ReLU as your default non-linearity between layers.

Once your models converge you can tweak your code in a fancy way and e.g. use skip connections, cyclic learning rates etc. The deeplearningbook 12 is also a great resource.