This is much easier done over water -- heavy-lift ships can move objects on the order of tens of thousands of tons routinely, and the largest examples of this type are able to handle objects in excess of 100,000 tons combined with immense bulk, up to and including an oil-platform-sized monster. Of course, you can also attach buoyancy devices to the beast until its seaworthy, then tow it with whatever quantity of towing vessels the thing's mass necessitates.
Over land, though -- such moves are far more difficult. Trains are the dominant industrial heavy-haulers of this day and age; no road-going vehicle can move the sheer amount of tonnage a modern locomotive consist-set can haul (well in excess of ten thousand tons, up to the thirty to fourty thousand ton range depending on how extreme your distributed power setup is). However, you're limited by the railroad loading gauge and by axle loading; this limit means that your monster has to fit within a 13-14' or so wide (up to perhaps 17' in the most generous of areas) by 23' high box, and to a practical maximum of a few hundred to a thousand tons with a well or Schnabel car and idlers; Schnabel car moves also limit the length to somewhat over 100' in order to avoid excessive in-train forces when negotiating curves.
If non-road-going vehicles are allowed, a crawler-transporter type vehicle can be used. These can handle several thousand tons of load, but would be limited to a dedicated, prebuilt crawlerway, and also to sizes in the 125' square range. If that's not an option, but large roads are available, the closest thing to a crawler-transporter that's still somewhat roadable would be a self-propelled modular transporter system. On-road load-limits for these range well into the hundreds of tons, and vehicle lengths and widths are limited by the design of available roads, but generally are smaller than crawler-transporters, especially widthwise. SPMTs are also agonizingly slow-moving compared to just about any other mode of transport discussed here, and transport over road subjects you to stringent height limits (13-14' unless you get an overheight permit in addition to the overwidth/slow-moving-load permitting you'd need for roading a SPMT, and even with an overheight permit, I doubt you could achieve more than 15-18' of clearance save for short distances on the order of a typical house move.)