  We prove gauge-invariant uniqueness theorems with respect to maximal and
normal coactions for $C^*$-algebras associated to product systems of
$C^*$-correspondences. Our techniques of proof are developed in the abstract
context of Fell bundles. We employ inner coactions to prove an essential-inner
uniqueness theorem for Fell bundles. As application, we characterise
injectivity of homomorphisms on Nica's Toeplitz algebra $\Tt(G, P)$ of a
quasi-lattice ordered group $(G, P)$ in the presence of a finite non-trivial
set of lower bounds for all non-trivial elements in $P$.
