We are making a college board game, and would like to know if we can use a few monsters from dnd to make our game. We don't use the same name as you do, just the images from online and the books.
No. The images are copyrighted, and you are using them in a way that would leave you with virtually no argument for fair use. The factors for fair use are set out in 17 USC 107, and they indicate that the courts would reject your use:
The purpose and character of the use, including whether it is of a commercial nature or for nonprofit educational purposes: There's no indication that your use would be for nonprofit or educational purposes.
The nature of the copyrighted work: Works of fiction and art are highly creative works at the heart of the policy for copyright protection.
The amount of the portion used in relation to the copyrighted work as a whole: You are apparently copying entire images, though I suppose you could argue that each image is just one small portion of a larger book or website.
The effect of the use upon the potential market for or value of the copyrighted work: You are trying to create a board game, putting yourselves basically in direct competition with the makers of D&D.
I generally prefer a pretty liberal interpretation of what constitutes fair use, but this just has virtually nothing that would make me comfortable arguing in your favor.
Many D&D monsters and creatures are based on creatures occurring in folklore and myth, such a vampires and trolls. Those are in the public domain, and anyone may use them freely. But images published as part of D&D, or by independent artists, are subject to copyright, and may not be used without permission. As the answer by bdb484 says, there seems no plausible case for a fair use exception to copyright here.
Note also that the specific descriptive text used in the D&D Monster Manual and other publications is protected by copyright, and may not be copied or closely paraphrased. This is true even when the creature being described is one from traditional folklore.
New creatures or monsters invented as part of D&D would be fully protected by copyright. While the general idea cannot be protected, anything based at al closely on a published description is likely to constitute copyright infringement.
If you were to copy content from published D&D books, a copyright suit might force you to stop distributing your game, and leave you with sizable damages to pay, depending on the exact facts.
You would be wise to invent your own monsters, or create your own versions of traditional monsters from legend and folklore.
As noted in other answers, no, you are not allowed to use these creatures under Fair Use. You could go back to their original mythological underpinnings (for those that have them), but you would have to take great care to make sure everything about them you describe comes from myth and not from D&D.
There is another option, however. Many Dungeons & Dragons monsters are available for use under the Open Game License. This does not cover images (at least not Wizards of the Coast’s images; some artists have released images of D&D monsters under the OGL), but it does cover their names, their stats, the names of their abilities, and their general “character.” It also does not cover certain particular iconic monsters, which Wizards of the Coast reserved as “product identity.” This would be beholder, carrion crawler, displacer beast, gauth, githyanki, githzerai, kuo-toa, mind flayer (illithid), slaad, umber hulk, and yuan-ti. It also doesn’t cover myriad other monsters that simply were never released in a book that got open-game treatment. But all of these monsters, for example, may be used.
Correctly following and using the Open-Game License requires some care. Read it carefully, and in particular pay close attention to the requirements in Section 15.
If this is a class assignment to create a game that you have no intention of distributing or selling, then I think you qualify for fair use. Within the context of a college class, it should qualify as educational.
If you are creating a game aimed at the college marketplace that you intend to distribute and/or sell, then it is more complicated. Obviously you can't use the copyrighted images in your product without permission. But can you use the images in a product prototype or mockup that is shown to potential investors or focus groups? This would almost certainly not count as fair use, but if you are only doing private viewings, and you make it clear that those images are placeholders, you probably won't attract any trouble.
If you want to avoid any problems, then find a starving art student that would love to be paid to create images for you. There are sure to be plenty around.