Are Ainz and his servants still leveling up the same way they were when they were killing monster to get exp in Yggdrasil?
Hmmm... To my understanding, Ainz and the high-tier minions (read those that are level 100) don't level up any further, as they are maximum level already. It's never mentioned that they 'get stronger' while others like the lizardmen and that weird hamster indeed do (the narrative comments several times that they are training to get stronger). Now, it is possible the New World has a higher level cap but insofar it hasn't been mentioned at all in the nine LN, the WNs nor the anime and manga. So Ainz ain't levelling nor are the floor guardians, but some of his minions do.
Lvl 100 was maxed level in the game, but the New world has different laws and something from the game manifest differently. This is because the new world isn't a game, but instead, an actual world that is trying to make sense of the game mechanics.
In the game, the minimum amount of experience a monster could give is 1 and also Ainz had 100% experience to level if the game allowed him to become level 101.
Ainz should have leveled already if he was gaining experience points, the only caveat is that what if the New world is giving humans or other monsters less experience. For example, if the new world gives humans 0.001 experience then it could still be possible, but there isn't anything that suggests that Ainz can level.
Last note, the author himself said Ainz is maxed level and he won't be able to level.
Reference to the translation, which has a reference to the original.
I was reading the books and Ainz is clearly saying he should have leveled up but didn't feel anything different so he concludes he can't level up. But I think he is wrong. He is a better fighter and he is doing things no spell caster would be able to do. Meaning he has obtained some fighter levels.
At smaller "levels" it is easy to see an increase in power but when you have 100 "levels" getting 1 more is not so evident. Also I think that in the new world there is no fix levels. In games you only get skills when you level up but now I think you learn the skill step by step for example at the middle of you leveling from lv2 to lv3 you can do the skill that you gain at lv3 but not as good.
There is an example that goes against this when Neia Baraja uses divine power for her archery it seems like an instant gain unlike Hamsuke constant training and step by step level up.
Of course a reason he would be able to be better at fighting but not level up could be because he is getting used to his powers and learning how the world works. Also gaining power from flavor text with no mechanical gain in game but true now. If that is true then it would look like leveling but only discovering his powers.