Can the basic transistor configs for small-signal amplification: voltage divider, collector feedback, self-bias, ever be made loud enough for driving audio for a speaker(not earbuds)? Or should you only try to do it with power amplifier configurations: class A, class B, etc..?
Well, a Class A power amplifier is actually the same configuration as a small-signal amplifier. You can use a voltage divider for the base, and/or collector feedback, self-bias (JFET or toob), and emitter degeneration. But to drive a speaker (typically 8 ohms), you need a pretty low output impedance, which means a high current. If you use a collector load resistor, it has to have a pretty low value, and with around half the supply voltage across it, it will dissipate a lot of heat and waste a lot of power. Ditto with the output device. A transformer in the collector improves things somewhat, but it must be designed so it doesn't saturate with the DC bias.
Another factor to consider is that bipolar power transistors have a relatively low current gain, and it drops at higher collector currents. Typical current gains of 10~20 are normal, compared to current gains in the hundreds for a small-signal transistor in a small-signal circuit. So for proper operation, a Class A power amp may need a more complicated bias circuit than a small-signal amplifier does.
Some audiophiles are prepared to live with these disadvantages because of the magical powers of Class A - specifically, no crossover distortion. But normal people consider it impractical for any significant amount of output power - the borderline is around half a watt I suppose - and so we use Class AB or Class B.
Or should you always have a small-signal amp function as pre-amp for a power amp?
Yes, you have to drive a bipolar Class A output stage with significant current, because of its low gain.
and how do you add more amplification stages without distorting the signal?
I'm not sure what you mean. I would drive a bipolar Class A output stage from an emitter follower, probably, which would in turn be driven from a voltage gain stage of some kind, if necessary. Every transistor adds some distortion, but the distortion in a Class A output stage will be the main factor, unless feedback is used.
Google Class A transistor output stage for more information.