Are there any rules for battlesuits (think of the Starship Troopers novel) or mechs (as in Battletech) in any of the Mongoose Traveller sourcebooks? If so, where?
Battlesuits already exist in Traveller, and are what is called "Battledress". The Central Supply Catalog has some varieties of Battledress that expand the basic options somewhat.
Mechs can probably be built with the new Vehicles supplement, but I don't have that supplement, so I'm only guessing.
The vehicle ( supplement5-6) book allows the design of combat walkers (mech) along with the 2300 AD hard suites, combat walkers and battle suites
Traveller mechs come in the form of "Oversized" and "Titan" armor, which are basically scaled-up versions of powered armor. For example:
StTPA-15, Standard Titan Combat Armor-15, 1620 kg, KCr 2400. AV 84 (MgT AV = 23).
"Titan" armor is approximately three times the size of standard armor. Thus a "Titan" suit may be 18' tall. Perhaps not quite in the 'mech' category.
Note that this data is from Traveller5's ArmorMaker chapter, but adapts fine into Mongoose Traveller.