Resolution isn't something that is as simple as setting the right value in your file. Basically those values in an image file (or other graphics artwork file) are simply a guide to the person who is rendering it as to how big you intended it to be in real life. You could take a 10 by 10 pixel image and simply claim that you intend it to be shown at a 24 inch by 36 inch poster-ish size, but it would look really badly. You need to have designed it to look good at those sizes.
Vector artwork is usually scalable to any size so you can stretch it to poster size and print it at the resolution of a professional press device - usually. Sometimes the artist was only drawing it at screen resolutions and never looked at what they did at large scales and so didn't notice that their lines didn't meet up very well at the corners when you view them large - but such issues are not common so generally vector artwork is considered fully scalable.
Images, on the other hand, store discrete samples. If your image has 5000 pixels across and you stretch it to 25 inches then you have 200 pixels per inch at that resolution. That might make a reasonable poster. If it has 800 pixels across and you stretch it to 24 inches then it only has 33 pixels per inch and that isn't going to look very good.
You "could", in fact but not recommended, stretch the image to that "size", but it will just show blocky pixelization artifacts. You can "resize" the image to have more pixels, but that is simply a combination of "stretching" it and then saving it with the added pixels. Basically, for images, you need (as close to as you can get) original versions of the images that originally had as many pixels as you can get. You'd probably ideally want at least 100 (original) pixels per inch of your intended printing output, but 200 or more would be better (and professionals would probably scoff at numbers that low).
So, your first step would be to get vector representations of either of the two images you used, or at least a high enough resolution version of them in an image format that your "pixel dimensions divided by the intended printing size" is good enough for the quality desired. And it would be best to deliver a vector version of the combined file (so that the vectors in any of the source art can be rendered at the desired final printing resolution by the printer itself) unless all of your original artwork was just pixel-based images anyway.
