I wish I had $10 for every time I was asked that question!
It can cost the same, or more, or less than it costs to buy or build a house in the U.S. How much does it cost to buy a house in Ohio? How much does it cost to buy a house in Dallas? It is impossible to answer to those questions either without knowing a whole lot more details.
The cost of a house, simply put, will depend upon what kind of house you want, what size of house, and where it is. The price of land varies tremendously. A tiny lot on the beach on the island of Roatan might cost vastly more than several acres in a secluded mainland location which, incidentally, might not have access to water or electricity.
If you want a replica of an 'American' style house complete with all the quality amenities, you could pay even more than it might cost you in the U.S. as you might have to import those quality items that aren't available here and might even have to bring in experts to install them.
Living in or near a big city or popular area will probably mean that labor costs will be higher while living in a smaller remote town will probably mean that material costs will be higher (lack of competition plus transportation costs). So even cost per square foot will vary a lot depending upon what part of the country you are considering.
I'm not a real estate agent and I don't have any reason to keep up with prices. Right now in La Ceiba, judging by the ads in the newspapers, there are many houses available in the US $50-60-70,000 range. As to whether those houses would suit your needs or whether you would want to live in those areas, I have no idea.
There are houses even less expensive than that, but if you are partial to electricity, like to have water at least most of the day, want a kitchen with more than 18 inches of counter space or a lot with more than a postage stamp-sized yard, you might have to increase your price range.
There are just too many variables for me to even attempt to guess! I would say, however, that if you are thinking you can build or buy a house for US $10-20,000, it ain't gonna happen! US $100-200,000 is more likely to get you a house like you are used to.
I have included a few articles on my blog about some of the colonias (neighborhoods) around La Ceiba. I plan to do more of that just because so many people seem to be interested in houses. I enjoy looking at houses and because we have so much new construction going on, there is a lot of material out there. In fact, I'll add a "Housing" topic in the sidebar to make the articles easier to find.
For those of you serious about moving to Honduras who want to see what is available, I have a few suggestions.
1. First and foremost, do not ever consider buying property in Honduras without seeing it in person (especially during rainy season), talking to neighbors, hiring a good attorney, and doing all the other due diligence (plus some) that you would perform anywhere else.
2. I always recommend that everyone come down and rent for 6 months to get familiar with the area and find out if living here is what you really want. Renting is cheap and much less expensive than finding out later that you've made a terrible mistake.
3. Google "Real Estate Honduras" or "Real Estate La Ceiba." Not all real estate companies have websites in English, so also Google "Bienes Raices Honduras."
4. The online Honduran newspapers include the classified advertisements (under Bienes Raices). Many properties are sold by owner. Ads won't tell you much, but may give you an idea of prices. (Here are the newspaper links.)
5. If you are taking my advice from #2, while you are here, drive around. See what areas you like. Talk to several agents. Look at as many houses as you can to see what is available in your price range. Talk to people that you meet. They may know of something available or may know of problems in the area that you are considering.
If you are interested in seeing a particular colonia, let me know. If it is close by and if I can, I'll do an article and take some photos of the houses and neighborhood in general. I won't do your due diligence or make appointments with real estate agents, though!
Now here is a house that you might be able to get for under US $10,000, but chances are that the homeowner does not own the property that it is sitting on.