I want to know if the unusual scenario of money orders written to myself would work as proof of sufficient funds, instead of the usual credit cards or bank statements. This is because I am currently in a situation where this is my only possible option and it is very lengthy to explain but I am hoping for a basic enough answer to help me along.
In short: we don't know as we are not border control and this is at their discretion but I have a suspicion.
You didn't specify a country but you don't need to.
The answer is no, no, no, no.
People, you want to be boring at the border. We see saw many of these questions trying to outsmart border control, regulations -- but the border guard have already seen everything you could possibly think of, ten thousand times over.
Most of the time, proof of funds won't arise these days at border control. Sure it will for visa request but at the border it's not usual any more: either you have a visa and thus already vetted or come from a visa exempt country where they presume you are good. Actual border refusals are exceedingly rare. Thus, if it does come up, it's an unusual scenario and just about the last thing you want in an unusual scenario is an unusual answer. The border guard will have seconds on spot to make a decision. They will err on the safe side and you can enjoy a swift trip home.
In other words, if they want to verify your ties to your home country and you come up with ... that? what do you think is going to happen?? Because that's what they are chiefly concerned about: are you going to leave or stay and become an illegal worker. (Beyond, of course, admitting dangerous people.)
This doesn't really add much to chx's excellent answer. But...
How can you possibly be in a situation where showing a money order is the only way to prove you have funds? Let's examine the possibilities? If you have good finances, but you've been dealing entirely on the basis of cash and have no statements, then stop travelling; open a bank account, get a credit card, start using them. When you've got a few months of statements start travelling. You can get a free credit card anywhere, and if you can't afford bank fees then you can't afford to travel.
The only alternative is that your finances are actually bad, and you've worked out some sort of scheme where you can obtain a money order just so you can show it to immigration. That's bad, and it's exactly the sort of thing immigration is trying to prevent.
I can think immediately of two ways this could be you trying to get around immigration rules - the money order may be fake, or you may have persuaded someone to write a real one for you on the promise that you will never cash it (or will pay it back). Both of those are immigration fraud. Believe me, if I can come up with those in a few minutes an immigration officer will take less then a tenth of a second to think of both of them.
When you actually enter into the Schengen area, you have to show (on demand, not always) that you have the funds for subsistence during your stay. Usually that means a form which hotels, or supermarkets, or restaurants are going to accept as payment. There are countries which accept telegraphic money orders. And others which do not.
But I agree with the answer by chx, people in "complicated" financial situations are not the kind of tourist or business traveler who are welcomed. If you genuinely have that money, and if you have no other way to transfer it, carry cash. Amounts over €10,000 must be declared, but they are legal.
Money orders are not very useful in international travel. Technically, you may be able to deposit them at a foreign bank, but even then it will taken some time for them to clear.
If you are looking for an option similar to money orders, travellers cheques could be somewhat better. In principle, they could be used for purchases or exchanged for cash in the country you're visiting. However, note that the use of travellers cheques is declining.
While travellers cheques would be relatively unusual nowadays as a proof of funds at the border, they would not be entirely unreasonable.