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Current usage

In current English, woke is the standard past tense of wake, both transitive and intransitive, causative or not; waked is marked as nonstandard (dialectical) or archaic, and it’s nowhere near as common as woke.

Current verbs

Waked vs. woke in current usage

In current English, woke is the standard past tense of wake, both transitive and intransitive, causative or not; waked is marked as nonstandard (dialectical) or archaic, and it’s nowhere near as common as woke.

An exception to this is when wake is not the inherited verb(s) discussed above, but rather a different verb derived (through normal zero-derivation) from a noun. Wake as a noun has at least two common meanings (etymologically unrelated): a vigil after the death of someone; and the trail of water or air left behind a vessel. When either of these nouns is used as a verb, the verb is a secondary, derived one, and such verbs are (nearly) always weak.

That means that the local community waked old Mrs. Smith last week after she passed away; you would never say that they *woke her. Similarly, you might possibly say that the ferry waked its way through the narrow strait; but certainly never in a million years that it *woke its way.
(Thanks to @supercat for mentioning this in the comments below.)

The words watch, (a)wake, (a)waken all share a common root. The Proto-Indo-European root was *u̯eǵ-, and its basic meaning approximately ‘to be strong/quick/lively/aroused/powerful’. It underlies for example Sanskrit वज: vájaḥ ‘power/force’, Latin vigil ‘watchful/awake’ (as in English vigil also), vigere ‘be lively’ (as in vigorous in English), velox ‘fast/lively’ (from *veg-lox; as in velocity in English).

The words watch, (a)wake, (a)waken all share a common root. The Proto-Indo-European root was *u̯eǵ-, and its basic meaning approximately ‘to be strong/quick/lively/aroused/powerful’. It underlies for example Sanskrit वाजः vā́ jaḥ ‘power/force’, Latin vigil ‘watchful/awake’ (as in English vigil also), vigere ‘be lively’ (as in vigorous in English), velox ‘fast/lively’ (from *veg-lox; as in velocity in English).

This is the reason why waken today has only a weak past form, wakened, while wake can have both strong woke and weak waked.

¹ There’s quite a bit of discussion about what the exact usage of these nasal formations were in Common Germanic. They are often based on nouns describing people or jobs, and they then mean ‘do/behave as X does’, a basically causative or factitive meaning; thus, in Old English, we get læcnian ‘heal’ from lǣċe ‘doctor’. But they are also used more or less as inchoatives from adjectives, as blacken ‘become black’ from black.

This is the reason why waken today has only a weak past form, wakened, while wake can have both strong woke² and weak waked.

¹ There’s quite a bit of discussion about what the exact usage of these nasal formations were in Common Germanic. They are often based on nouns describing people or jobs, and they then mean ‘do/behave as X does’, a basically causative or factitive meaning; thus, in Old English, we get læcnian ‘heal’ from lǣċe ‘doctor’. But they are also used more or less as inchoatives from adjectives, as blacken ‘become black’ from black.

² As Jon mentions both in his answer and a comment here, woke, phonemically /woʊk/, is not quite regular from the Old English wóc. Some analogy with similar-sounding verbs like break, speak, and steal (which did sound the same earlier on, though they’re different now) took place at some point. Middle English wook or wooke or woke can be regular from wóc, assuming that they represent /wuk/, which is what the Old English form should give—but that’s not necessarily a given, considering the vagaries of Middle English spelling.