Nebula and galaxies using 70mm scope
You can see some of them with a naked eye. Many of the Messier objects, including galaxies and nebulae are observable even without any telescopes. As for others, if Charles Messier could catalog them in 1771 with a 4 inch refractor, you should see most using your 3.3 inch reflector too given good observation conditions, knowing where to point and using a properly collimated and otherwise maintained telescope.
Messier was from the Northern hemisphere and you seem to be closer to the equator judging by information you provide in your profile, so you shouldn't have problems seeing these objects either, and there are equally interesting objects also in the Southern skies that you could observe. Some of the easiest recognizable on the Northern skies are the Andromeda galaxy, or Messier 31, and the Orion Nebula, or Messier 42. You should also be able to discern quite a lot of detail of other astronomical bodies, including e.g. Pleiades, or Messier 45 which is also visible to the naked eye and many astronomers use to determine observational conditions and their visual acuity by.
Whether you'll be able to see them depends on the levels of light pollution in your area. As TildalWave mentioned, a number nebulae and galaxies are perfectly observable with the naked eye so unless you live somewhere very bright, you should be fine. Under really dark skies, objects like M31 are very easy to find with the naked eye. Where I live, I hardly see it with a bright binocular due to very poor seeing, induced by a large number of shopping centres fond of pointing powerful searchlights at the sky for whatever reason.
As to how much you'll be able to see, you can get a general idea of what you should be able to see in ideal conditions by calculating your telescope's limiting magnitude
In reality, you'll also have to factor in the quality of the optics (mainly transmission), both the telescope and the eyepieces. Of the two you mentioned in your question, you should use the 25 mm one. It will give you a lower magnification, a bigger field of view (better for most bright nebulae and galaxies due to their often significant angular dimensions)
Here's a highly configurable calculator that you can use.
Since you live in the northern hemisphere, objects from the Messier catalogue are great candidates to begin your observations with.