Learn Russian: Музыканты не таскают рояли сами, для этого есть грузчики. - Musicians do not haul grand pianos themselves; there are movers for this.

The sentence describes a general, habitual fact: musicians do not typically haul pianos around as a rule. Since there is no specific single trip in one direction being described, the multidirectional verb таскать is required.

Is рояли in the nominative or accusative case here?

It is in the accusative case, acting as the direct object of таскают. Because рояль (grand piano) is a masculine inanimate noun, its accusative plural form is identical to its nominative plural form (рояли).

Could I use себя instead of сами to mean "themselves"?

No. Сами (the nominative plural of сам) is an emphatic pronoun meaning "they themselves do the action". If you used the reflexive pronoun себя, it would mean the musicians are physically hauling each other as the object, rather than hauling the pianos!

Why is есть used in the second clause? Doesn't Russian usually omit the verb "to be" in the present tense?

While the "is/are" linking verb is usually dropped to say what something is, есть is kept when asserting the existence or availability of something. Here, it translates to "there are" or "there exist" movers for this purpose.