Transformer output connected to another transformer. Measuring 'Real Power' at input of first transformer
The real power that you measure when there is no load connected to a transformer is the "iron losses" in the laminations consisting of hysteresis and eddy-current losses. The reactive power is due to the magnetization of the core. There will be a small copper loss in the primary due to the magnetizing and core loss current.

The total losses for one transformer feeding another will include some copper losses in the first transformer due to the total current supplied to the second transformer. The real and reactive power of the second transformer should be reflected unchanged in the measurements made on the primary of the first transformer.

Here is something to compare your results with:

I measured the  no-load losses for a 150 VA transformer with a 120 V, 60 Hz primary. At 122.2 V, the input current was 0.13 A, the power was 5.3 watts, the apparent power was 16.6 VA and the power factor was 0.31. The data was taken with a Kill-A-Watt. The transformer weighs about 6.5 lbs and has a 3-3/4 X 3-1/8 X 1-7/8 inch lamination stack.

Data for a transformer rated about 100 VA was 3.1 W and 9.1 VA. A transformer rated 25 or 50 VA measured 3 W and 10.4 VA at no-load. The two larger transformers were for industrial products sold to paper mills and auto manufacturers. I believe the small transformer was used in a consumer product.

Comparison of Kill-A-Watt data with data taken with other meters leads me to believe that it is accurate within 1 to 3 percent.

If the meter indicates "lots" of power with nothing but the transformers connected and they aren't burning up, there must be something wrong with the meter or your use of it. My Kill-A-Watt has a Watt/VA button that toggles the display between Watts (real power) and VA (apparent power).

Here is a Kill-A-Watt meter showing watt and VA readings for a CFL lamp.