Onkyo and Integra brands are made by the same company. Of the receivers you listed, the Onkyo 818 is the only one which includes Audyssey MultEQ XT32, the top-of-the-line of Audyssey's room equalization software. The improvement provided by the ..32 version over the XT version has gotten rave reviews from just about everyone who's listened to it.
Yamaha's competing YPAO room equalization software doesn't do anything for subwoofers or frequencies below about 32Hz.
Marantz SR7009/7.1.4/FH+TM/DefTech PM1000/LCR+TM amped