It would be best to know exactly what you have and the areas where you got them from in order to answer your question the best.
Yes, you can use hay or straw for mulch. But, I wouldn't advise putting them around trees or piling them very thick because they are favorite types of nesting and hiding places and materials for rodents and insects of various sorts. Also, hay can contain a large number of weed seeds. You could use them in thin layers in various types of flower or vegetable gardens though in order to retain moisture. I don't think that either of them are very ornamental. They will break down in time and can also be worked into the soil in the fall so as and aid to the soil for the next years plantings of flowers or vegetables.
If you are going to use any mulch around trees, I would suggest using a bark variety and keeping it at least six inches away from the trunk of the tree so that the bottom of the tree doesn't rot out because of the retained moisture.
There is also some excellent information on the following links concerning using straw or hay as a mulch.
How to use mulch Mulch Mulching Tips Mulches for the Home Vegetable Garden iCanGarden.com Straw for mulch? - Cutting Garden Forum - GardenWeb Publication: Mulches for the Home Landscape Use of Straw as Mulch: A Cover Story Control Weeds in the Garden and Landscape
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