Editar/Eliminar datos Firebase sobre un RecyclerView

Considero que sería más adecuado que el adapter pasara el aviso completo a la vista en el onClick por medio de un listener. Al final te paso un ejemplo. No obstante, también podrías enviarle el Aviso completo a la clase MyMenuItemClickListener y utilizarlo después en el onMenuItemClick

private void showPopupMenu(View v, Aviso aviso)
    {
        PopupMenu popup = new PopupMenu(mContext, v);
        MenuInflater inflater = popup.getMenuInflater();
        inflater.inflate(R.menu.menu_avisos, popup.getMenu());
        popup.setOnMenuItemClickListener(new MyMenuItemClickListener(aviso));
        popup.show();
    }
...
...
...
class MyMenuItemClickListener implements PopupMenu.OnMenuItemClickListener{

private Aviso aviso;

public MyMenuItemClickListener(Aviso){
  this.aviso = aviso;
        }

        @Override
        public boolean onMenuItemClick(MenuItem item) {
            Intent intent = null;
            switch (item.getItemId())
            {
                case R.id.action_eliminar:
                    Toast.makeText(mContext, "Eliminar Aviso (Test) " + aviso.getAviso(), Toast.LENGTH_SHORT).show();
                    return true;

...
...
...

Te paso un ejemplo de cómo puedes pasar Aviso a través de un nuevo listener. En el ejemplo, la entidad se llama Goal

Adapter

public class GoalListAdapter extends RecyclerView.Adapter<GoalListAdapter.ViewHolder> {

    private List<Goal> goalList;
    private GoalItemClickListener goalItemClickListener;

    public GoalListAdapter() {
    }

    public void setGoalList(List<Goal> goalList) {
        this.goalList = goalList;
        notifyDataSetChanged();
    }

    public void setGoalItemClickListener(GoalItemClickListener goalItemClickListener) {
        this.goalItemClickListener = goalItemClickListener;
    }

    @Override
    public ViewHolder onCreateViewHolder(ViewGroup parent, int viewType) {
        View view = LayoutInflater.from(parent.getContext()).inflate(R.layout.goal_list_item, parent, false);
        return new ViewHolder(view);
    }

    @Override
    public void onBindViewHolder(ViewHolder holder, int position) {
        Goal goal = goalList.get(position);
        holder.setClickListener(goal, goalItemClickListener);

        holder.tvTitle.setText(goal.getTitle());
        holder.tvDescription.setText(goal.getDescription());
    }

    @Override
    public int getItemCount() {
        return goalList.size();
    }

    public void add(Goal goal){
        if (!goalList.contains(goal)){
            goalList.add(goal);
            notifyDataSetChanged();
        }
    }

    public void update(Goal goal){
        if (goalList.contains(goal)){
            goalList.set(goalList.indexOf(goal), goal);
            notifyDataSetChanged();
        }
    }

    public void remove(Goal goal){
        if (goalList.contains(goal)){
            goalList.remove(goal);
            notifyDataSetChanged();
        }
    }

    public class ViewHolder extends RecyclerView.ViewHolder {

        @BindView(R.id.goal_list_item_tv_title)
        TextView tvTitle;
        @BindView(R.id.goal_list_item_tv_description)
        TextView tvDescription;

        private View view;

        public ViewHolder(View itemView) {
            super(itemView);
            this.view = itemView;
            ButterKnife.bind(this, view);
        }

        private void setClickListener(final Goal goal, final GoalItemClickListener listener){

            if (listener != null) {
                view.setOnClickListener(new View.OnClickListener() {
                    @Override
                    public void onClick(View v) {
                        listener.onItemClick(goal);
                    }
                });

                view.setOnLongClickListener(new View.OnLongClickListener() {
                    @Override
                    public boolean onLongClick(View v) {
                        listener.onItemLongClick(goal);
                        return false;
                    }
                });
            }
        }
    }
}

Vista public class GoalListActivity extends BaseActivity implements GoalListView, GoalItemClickListener {

private static final String TAG = GoalListActivity.class.getSimpleName();

@BindView(R.id.goal_list_activity)
CoordinatorLayout coordinatorLayout;

@BindView(R.id.goal_list_activity_toolbar)
Toolbar toolbar;

@BindView(R.id.goal_list_activity_rv_concepts)
RecyclerView rvConcepts;

@Inject
GoalListPresenter presenter;

@Inject
GoalListAdapter adapter;

@Inject
LinearLayoutManager linearLayoutManager;

@Inject
VerticalDividerItemDecoration dividerItemDecoration;

@Override
protected int getToolbar() {
    return R.id.goal_list_activity_toolbar;
}

@Override
protected int getLayout() {
    return R.layout.goal_list_activity;
}

@Nullable
@Override
protected BasePresenter getPresenter() {
    return presenter;
}

@Override
public void setUpComponent(AppComponent appComponent) {
    DaggerGoalListComponent.builder()
            .appComponent(appComponent)
            .goalListModule(new GoalListModule(this))
            .build()
            .inject(this);
}

@Override
public void setUpView() {
    rvConcepts.setLayoutManager(linearLayoutManager);
    rvConcepts.addItemDecoration(dividerItemDecoration);
    rvConcepts.setHasFixedSize(true);
    rvConcepts.setAdapter(adapter);

    adapter.setGoalItemClickListener(this);
}

@Override
public void navigateToConceptAddView() {
    Intent intent = new Intent(this, GoalAddActivity.class);
    startActivity(intent);
}

@Override
public void showConceptList(List<Goal> goalList) {
    adapter.setGoalList(goalList);
}


@OnClick(R.id.goal_list_activity_fab)
public void onClick() {
    presenter.showConceptAdd();
}

@Override
public void showError(String message) {
    Snackbar.make(coordinatorLayout, message, Snackbar.LENGTH_LONG).show();
}

@Override
public void onItemClick(Goal goal) {

}

@Override
public void onItemLongClick(Goal goal) {

}

}

Como puedes observar, la vista setea el adapter en el recyclerview y setea la propia vista como GoalItemClickListener (adapter.setGoalItemClickListener(this);) ya que lo implementa

@Override
public void onItemClick(Goal goal) {

}

@Override
public void onItemLongClick(Goal goal) {

}