This isn't weird looking. It's what normal MCU code actually looks like.
Arduino code is the weird stuff, with functions that access the MCU control registers indirectly. While this is somewhat "nicer" looking, it's also much slower, and uses a lot more program space.
The mysterious constants are all described in great detail in the ATmega328P datasheet, which you really should read if you're interested in doing anything more then occationally toggling pins on an arduino.
Select excerpts from the datasheet linked above:
So, for example, TIMSK1 |= (1 << TOIE1); sets the bit TOIE1 in TIMSK1. This is achieved by shifting binary 1 (0b00000001) to the left by TOIE1 bits, with TOIE1 being defined in a header file as 0. This is then bitwise ORed into the current value of TIMSK1, which effectively set this one bit high.
Looking at the documentation for bit 0 of TIMSK1, we can see it is described as
When this bit is written to one, and the I-flag in the Status Register is set (interrupts globally enabled), the Timer/Counter1 Overflow interrupt is enabled. The corresponding Interrupt Vector (See ”Interrupts” on page 57) is executed when the TOV1 Flag, located in TIFR1, is set.
All the other lines should be interpreted in the same manner.