Mayuri is by far the craziest captain of the Gotei but I wouldn't say he is the strongest or the weakest Captain. They all have their bonuses and their faults. Of the current Gotei this is how I think some of his fights would go down.....
1st Division - Captain Commander - Shunsui Kyoraku: Mayuri would have a relatively hard time against Shunsui simply because you never know what game Katen Kyoketsu is going to want to play and when. But when it comes to using the Bankai that would be relatively easier, since everyone knows that Shunsui will try his best not to use it in the presence of others, why is that? well we will find out ssoon hopefully lol.
2nd Division - Suì-Fēng: Her sheer speed would be a hassle for Mayuri but with enough preparation for the fight he would be able to hold his own even with that nasty ability of her Shikai. As for her Bankai he would have a relatively easier time dealing with that one as he would just have to make sure he stays close, I don't think she would be willing to take herself out with Mayuri using her Bankai, as we have only seen her use it when she has some distance between her and her opponent or there is a barrier saving her from the blast.
3rd Division - Rōjūrō "Rose" Ōtoribashi: One of the 3 current Vizard Captains of the Gotei. How his hollow powers amplify (or amplified) Rose's abilities has yet to have been shown so we are clueless on this front. But with his Zanpaktou's abilities to attack through sound waves makes it a pain for Mayuri (unless properly prepared for this fight). As for his Bankai, I honestly think Mayuri would have a difficult time with this even if he was properly prepared for it, unless he out right removes his ear drums then he won't have too much of an issue.
4th Division - Retsu Unohana: Currently deceased by the hands of Kenpachi Zaraki. As for her abilities I honestly don't know how she would fair against Mayuri as there wasn't a proper explanation of her Zanpaktou abilities. All we know about it is that she was able to revive her opponent several times before being killed.
5th Division - Shinji Hirako: Yet another of the Vizard Captains of the Gotei. Now unlike the others we know more about his abilities with his mask, that amplify his speed, power, as well as being able to fire off Cero's. Now for his Shikai, I believe that Mayuri would have little to no defense against this man's ability outside of stripping himself of his sense of smell, but that would still leave him to deal with the other abilities, no bankai has been revealed as of yet for Shinji. This would end up being one of the more difficult fights for Mayuri in the end.
6th Division - Byakuya Kuchiki: A Shunpo master, and the man with the Zanpaktou that counts as a thousand blades. To be honest, I don't see anyway Mayuri would be able to win this fight, even with extraordinary preparation time. And Byakuya is even one of my least favorite Captains.
7th Division - Sajin Komamura: The Werewolf Captain of the Gotei, now in all honesty I don't think he would last too long against Mayuri even if he goes into his humanoid form. Yes, Sajin is quite easily one of the physically strongest Captain's, as shown when he flipped the released form of Choe Neng Poww, but against a man like Mayuri, I think Sajin could take out Mayuri's Bankai at the cost of his life, or health.
8th Division - : There is as of recent now Captain for this division so for the previous captain, read the 1st Division Captain Commander, Shunsui Kyoraku.
9th Division - Kensei Muguruma: The third and final (as for now) Vizard Captain of the Gotei. All that has been shown for his Hollow mask is an increase in his speed and already remarkable strength. As well as being the only Captain to have gone in a full Hollowfied form, which as well vastly increased his strength, speed and punches. Now if it came to a physical fight, Mayuri wouldn't stand a chance against Kensei. So for this fight Mayuri would half to prepare himself for this fight as we all know several of his bones will be destroyed. Kensei's bankai from what we know would be an annoyance at least for Mayuri, but its destructive capabilities would be a major hassle for Mayuri.
10th Division - Toshiro Hitsugaya: Alright to be fully honest here, I don't think Mayuri would stand too long of a chance against Hitsugaya. Albeit he isn't as smart as Mayuri, but he is more then enough of a match against the mad doctor. Hyorinmaru's abilities would be more than enough to put Mayuri on the run, until he is turned into a frozen human pop-sickle.
11th Division - Kenpachi Zaraki: This fight I would have to give to Mayuri, yes Kenpachi is a monster, he is crazy strong but in the end he would fall to Mayuri's unorthodox form of fighting and willingness to manipulate his body in the name of science for the fight.
12th Division - Mayuri Kurostuchi: Yeah....no need for this, as this is his division he has probably made clone sof himself to run weird and freakish tests on in combat.
13th Division - Juushiro Ukitake: This fight as for now I would have to leave as a draw, since we don't know too much of Ukitake's abilities outside of the fact that along with Shunsui and Unohana he is one of the oldest captains of the Gotei and one of the first to graduate Ol' Yama-jii's academy.