Learn Swedish: Sträck på dig och titta upp.

When you give a command using a reflexive verb, the reflexive pronoun has to match the person you are talking to. Since commands are directed at the listener, the generic pronoun sig (oneself) changes to dig (yourself).

Why is the preposition på required here? Can I just say sträck dig?

sträcka på sig is a specific expression meaning to stretch your body, like when you wake up or fix your posture. If you drop på and just say sträcka sig, it usually means to reach for something (like reaching for a cup on a high shelf) or to pull a muscle.

Why does the command form sträck drop the final letter a, but titta keeps it?

To form the imperative (command) form, you use the verb's stem. For Group 1 verbs like titta, the stem naturally ends in an a, so the imperative is just titta. For Group 2 verbs like sträcka, the stem ends in a consonant, so you drop the a from the infinitive, giving you sträck.

Since both sträcka på and titta upp act as phrasal verbs, which words get the emphasis when speaking?

In Swedish phrasal verbs (partikelverb), the stress almost always falls on the particle. Therefore, you should emphasize the words på and upp when saying this sentence aloud, leaving the verbs and the pronoun unstressed.