The phrase hypothetically speaking is used to refer to a hypothesis. Both conditional sentences you provide can be considered to be a hypothesis in the form of if.../then... They both "predict" that if one thing happens, then something else happens.
1 Hypothetically speaking, if I finish my homework by dinner, (then) I will be able to watch TV.
2 Hypothetically speaking, if I finished my homework by dinner, (then) I would be able to watch TV.
The difference in the two sentences is that the first is a real conditional and the second is an unreal conditional. In unreal conditional sentences, the if-clause uses a past tense form, and a modal in the main clause.
These two terms reflect the speaker's attitude. The real conditional does not specify any particular attitude. Thus the speaker leaves open the possibility that the proposition may come true. Sometimes this kind of conditional is called an open conditional. The unreal conditional expresses that the speaker has some doubt about the proposition. In the unreal conditional (If I finished..., then I would be able...) indicates that the speaker has some doubt (is not sure) that he can finish his homework. (This explanation of real versus unreal is based on The English Verb (2nd edition), upon which this answer is heavily dependent).
Let's look at another example of real versus unreal:
3 Hypothetically speaking, if Donald Trump is elected president, (then) will you be happy?
4 Hypothetically speaking, if Donald Trump were elected president, (then) would you be happy?
In the real conditional (sentence 3) the sentence does not comment upon the speaker's attitude toward the truth of the hypothesis. In the unreal conditional (4),the speaker indicates some doubt that Trump will become president and thus uses the past tense form in the if-clause and a modal (here, would) in the main clause.
Not all conditional sentences are hypothetical or predictive. Some refer to one thing that can be inferred from another thing. One example of this is a 'past real' conditional.
If I finished my homework by dinner, (then) I was able to watch TV.
Here the truth of one proposition (I was able to watch TV) is inferred from the truth of the other (I finished my homework by dinner).
So, hypothetically speaking wouldn't be appropriate here, since there is no prediction involved.
Of course English speakers are free to stick the two words hypothetically speaking before any sentence, and it doesn't have to equate with the grammatical explanation I've used here.
Hypothetically speaking I want to move to California does not express a hypothesis in the sense used in this answer.