Smells are (sometimes complex) mixtures of chemicals, but I don't know anything about chemistry and don't have much advice there.
But, in general, your approach could be to try and find various combinations of things that smell like what you're looking for, possibly through experimenting. In some cases you might even be able to use the item itself. This is assuming you can't find a way to store smells (maybe somebody else will have an answer for that). For example:
Sometimes you may be able to get the actual item that smells. If you can find a container that allows air to pass through but not the material itself you can put a fan behind it. For example, put a bunch of grass clippings in a fine mesh bag (examples: strainer bags, filter bags, wrapped in cheesecloth, etc., or take a trip to the local fabric shop and see if there's a fine mesh fabric you can use). To enhance the smell:
- Consider crushing, grinding, smashing, etc. the material, if applicable. For example, finely chop the grass, or use a mortar and pestle, or crush a bag of it under a rolling pin or something (or heck, run it over with a car), etc.
- Store it in an airtight bag until you're actually ready to use it, to preserve the odors as long as possible.
In certain cases, such as if the item is a liquid, you may be able to boil it on the spot with a portable stove. For these types of materials you either wouldn't want a fan (let it fill up the room), or put the fan in a location that isn't going to interfere with the boiling. (Btw, if you're fortunate enough to have access to a good portable induction cooktop, nothing will beat that in terms of safety, convenience, and efficiency).
The thing I think you might have the most luck with is: Incenses, oils, and scented candles. If you have an incense or candle shop around, go check it out. All of these are very convenient to use, good at dissipating smells into the air, and most usefully, a lot of candles especially are already formulated to emulate certain smells. Incense is generally very cheap, candles unfortunately can get a little pricey sometimes. You'll want to experiment, possibly with combinations, to make sure the smell is accurate and also not too "fake" smelling or cloying (unless that's your goal). In this case a tiny fan (especially with incense) can help distribute the smell more quickly. Anecdotally, I've found that one of the biggest triggers for thinking a smell is fake is if the smell is too strong, so you may have to come up with a way to control its distribution, for example by venting in fresh air to dilute the smell, or by lighting a candle only for a short while, etc.
As for experiments, watch out for olfactory fatigue during testing, as well as drying out your sinuses. Also, you might want to have another person or two give you their opinions. Others' opinions can be valuable here. I'd structure any tests with other people by stating what environment they should imagine themselves in (or just setting it up around them) then asking them what they smell. For example: "You are in a cave in the middle of a forest, it is slightly humid, cool, and dark, you hear the sound of a stream bubbling nearby and the wind whistling past the entrance. Describe what you smell."
If you just say "Hey does this smell like grass?" you run the risk of severely biasing their response. If you just say "What does this smell like?" you may get some strange results as smells can get weird with no context.
Hopefully this gives you some good starting ideas, or is at least somewhat helpful. Sounds like an interesting project. Good luck!