The 6ft 4in flanker is currently with Gallagher Premiership side Bristol Bears but has agreed a two-year deal with Edinburgh.
Australian-born but Scots-qualified, Haining previously featured for Jersey Reds, joining the Bears in the summer of 2017.
The back-rower played a key role in helping Bristol return to English rugby’s top flight in 2018, and has made seven appearanecs so far this term, with one try to his name.
He said: “When I spoke to Richard Cockerill about the direction and ambition of the club, it really excited me. I’m looking forward to moving to Edinburgh and starting pre-season in June - I can’t wait to get stuck in.”
Cockerill said: “Nick is someone I’ve been looking at for a while. He’s a big boy, carries the ball very well and is a good footballer.
“He’ll add some further strength in depth in that back-row where we’ve got a lot of internationals. He’s a very good player and he’s keen to put his hand up and try to push himself into the national squad as well.”
Captain of the Fiji Sevens team, Kalione Nasoko was named in the HSBC World Rugby Sevens Series Dream Team in 2017 and 2018, and also joins the Capital side on a two-year deal.
Standing 6ft 3in tall, the 28-year-old Nasoko has played 142 Sevens matches, scoring 63 tries and picking up winners’ medals in 2017/18 at Hamilton, Hong Kong, London, Singapore and Vancouver.
Fiji were also runners-up at the 2018 Commonwealth Games.
Nasoko said: “I’m very excited by the opportunity to join Edinburgh. I am friends with Viliame Mata and he has said great things about the club - I can’t wait to get started.
“This is a great opportunity, and after many years on the Sevens circuit, I can’t wait for this new challenge in Scotland. Everyone sounds very welcoming and I am looking forward to running out in front of the Edinburgh fans.”
Cockerill added: “Kalione is a tremendously exciting player. He’ll predominantly play as a winger, but he has also played at 13 and will bring something different to our back-three. He gives us a little bit more of an x-factor and, as you see with the good teams around Europe, you need that type of threat.”
Nicknamed “The Sledgehammer”, Sau is a policeman by trade and has been plying his trade for French TOP14 side Perpignan since May 2018. Like Nasoko, he is a key part of the Fiji Sevens side, and has contributed 37 tries in 58 Sevens games.
A winner in Hamilton, Hong Kong, London, Singapore and Vancouver, Sau cut his teeth playing rugby league with Kautoka-based Saru Dragons before spells with Red Rock and Fiji Police.
The 29-year-old has also represented the Fiji national team, scoring a hat-trick in a 68-7 victory over Uruguay.
Sau said: “I’m really excited by the opportunity to join Edinburgh and to test myself in the Guinness PRO14 and in Europe too. After speaking with Richard Cockerill and my friend Viliame Mata, I knew it would be a great move for my rugby career and also for my family. I can’t wait to work hard in the summer to earn a place in the team next year.”
Cockerill added: “Anyone who has watched Sevens will know Eroni. He’s a very strong and powerful runner, he’s tough and very combative.
“A nickname like “The Sledgehammer” gives you an idea of what he does with and without the ball, and I’m delighted he’s chosen to join Edinburgh and be part of what we’re building here for next season and beyond.”
Mike Willemse needs less of an introduction to Edinburgh fans, having spent the past 18 months with Port Elizabeth-based PRO14 side Southern Kings. The hooker, who has been capped by South Africa Under-20s, has featured 36 times for Kings, scoring five tries.
Likened in style to Stuart McInally, the 26-year-old Willemse cut his teeth at Eastern Province Kings, playing amateur rugby with UCT Ikey Tigers in the Varsity cup, before joining Western Province in 2013. The Cape Town native has also turned out for the Stormers in Super Rugby, and Golden Lions.
On joining Edinburgh, Willemse said: “I’m truly ecstatic to be joining such a prestigious club with such a rich history.
“It’s an awesome opportunity for me to progress my rugby career. It’s easy to see the professionalism as well as the upward curve that the team and squad is currently undergoing.
“Working with Richard Cockerill is something that I’m really looking forward to. I have no doubt that he will have a positive influence on my personal game and I look forward to learning as much as possible.”
Cockerill added: “Mike has got a lot of experience in Super Rugby. He’s a very competent hooker and is all-action, very good over the ball and extremely dynamic.
“We’re delighted to have him. We’ve got a good selection of Scottish hookers, but Mike is a guy who’ll be with us all year round and will no doubt push everybody to the next level.”
Willemse will team up with countrymen Jason Baggott, prop Pierre Schoemann, fly-half and fellow Golden Lions alumnus Jaco van der Walt and wing Duhan van der Merwe.