Travelling to Malta from Kenya next month, concerned about my visa application

Difficult to know if you will get a visa. Your position is less than ideal but we can't predict exactly what will happen.

Regarding the supporting documents, you need to establish three things:

1. What the purpose of the trip is (that's what the letter of invitation is for)
2. That you have sufficient “means of subsistence” for your stay and to return to your country (having a return flight and accommodation already booked and paid for would go a long away towards fulfilling this requirement)
3. That you intend to leave the Schengen area in time and return to your country of residence.

You really need to address all three requirements. Therein lies the rub: Employment, tax returns, etc. do not only show that you can get enough cash for the trip, they also show you have a stable situation to return to (point 3). So they are strongly recommended even if the costs for your trip are fully covered. The letter of invitation is crucial, the details of the hotel, etc. are good but on their own they are not enough.

There is no definitive list of what you should provide, basically the more the better. A good job is most important but showing that you have family ties in your country of residence – young kids or a wife/husband, parents won't do for a young man or woman – or that you own real estate could help too. Without that and without employment or proven income (even with cash on hand and/or everything paid for), the consular officer processing your application might decide that the risk that you would immigrate illegally is too high and refuse the visa.

Also, I guess you knew that already but applying to the Austrian embassy is indeed the right way to proceed, your application won't be rejected for that reason.