How does the 'relentless' rule work for Leman Russ tanks? Can the Leman Russ move and fire all weapons or is it like every other tank which can't move and fire it's ordinance weapon?
First of all, everyone can move and shoot Ordnance. No special rules required. What they cannot do is fire Ordnacne (moving or not) and fire another weapon as well.
As to your questions, I'm assuming you actually mean the Lumbering Behemoth rule?
Simply put, it allows the Leman Russ to fire it's main turret gun along with any other weapons it is allowed to fire, even if that main turret gun is Ordnance. Here's a chart:
Standing still, shoots everything, Turret (even if Ordnance), Hull, sponsons, pintles, doesn't matter. It can shoot everything.
Moved up to 6" (Combat speed). Can shoot one main gun plus any defensive weapons PLUS the turret main gun, even if it's Ordnance.
Moved over 6", nothing, zip nada, can not shoot. This ain't PotMS here.